HSF.IF.A.1: Understanding Functions, Domain, Range and f(x)
In plain English: HSF.IF.A.1 is the Common Core functions standard that asks students to understand what a function is: a rule that assigns each element of its domain exactly one element of its range. Students read f(x) as the output for the input x and see that the graph of f is the graph of the equation y = f(x). It is usually taught early in Algebra I.
Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x).
Common Core State Standards for Mathematics · Domain: Interpreting Functions (IF) · Cluster: Understand the concept of a function and use function notation Also written as HSF-IF.A.1 or F-IF.1 · Official standard
Students build the definition of a function from everyday rules and then test it in four representations: sets of ordered pairs, tables, mapping diagrams and graphs. The focus is on the two words that do the work in the definition: each input in the domain gets an output, and it gets exactly one. Students see that two inputs sharing an output is allowed, while one input with two outputs is not.
The second half introduces the notation f(x) as the name of the output that f assigns to x, and connects it to the graph: the graph of f is the graph of the equation y = f(x), so a point (a, b) lies on the graph exactly when f(a) = b. The vertical line test comes out of this connection rather than being memorized as a separate rule.
Learning Objectives
By the end of this lesson, students will be able to:
Decide whether a relation given as ordered pairs, a table, a mapping diagram, a graph or a verbal rule is a function, and justify the decision with the words input and output
Identify the domain and range of a function given as a finite set of ordered pairs or a table
Explain that f(x) names the output of f for the input x, and read values such as f(3) from a table, a mapping or a graph
Explain why a point (a, b) is on the graph of f exactly when f(a) = b, and use this to test points and to justify the vertical line test
Prior Knowledge Required
Students should already be comfortable with:
Understanding a function as a rule that assigns each input exactly one output 8.F.A.1
Evaluating expressions for given values of the variable 6.EE.A.2
Plotting ordered pairs in all four quadrants of the coordinate plane 6.NS.C.8
Reading a table of values and finding patterns in it
Project a picture of a school vending machine keypad and ask students to think about the rule that links buttons to snacks before you give any definition.
Warm-Up Prompt
"When you press B4, the machine drops a bag of pretzels. Would the machine still work well if B4 sometimes dropped pretzels and sometimes gum? Is it a problem if B4 and C2 both drop pretzels?"
Give students two minutes to argue in pairs. Draw out the contrast: one button that can give two different snacks makes the machine unpredictable, but two buttons that give the same snack cause no trouble. Write the buttons in one column and the snacks in another, connect them with arrows, and name the picture a mapping diagram. Tell students the buttons play the role of the domain and the snacks the role of the range.
Direct Instruction20 minutes
The definition. A function from a set called the domain to a set called the range assigns to each element of the domain exactly one element of the range. Underline both phrases: every input must get an output, and no input may get two. Show the idea in four forms: a set of ordered pairs, a table, a mapping diagram (Diagram 1) and a graph (Diagram 2).
Notation. If the function is named f and x is in its domain, f(x), read "f of x", names the output that f assigns to x. It is not f times x. If f sends 3 to 10, we write f(3) = 10.
The graph. The graph of f is the graph of the equation y = f(x): all points (x, y) with x in the domain and y = f(x). So a point (a, b) is on the graph exactly when f(a) = b. Because each x has only one y, no vertical line can meet the graph of a function in more than one point. Work through the examples below, asking students to predict each answer first.
Ordered pairs that form a function
Is {(1, 4), (2, 7), (3, 4), (5, 9)} a function? Give its domain and range.
Equation: Yes: each first coordinate appears once. Domain {1, 2, 3, 5}, range {4, 7, 9}
Ordered pairs that are not a function
Is {(2, 3), (2, -1), (6, 0)} a function?
Equation: No: the input 2 is assigned two outputs, 3 and -1
Reading f(x) from a table
A function f has the table x: -2, 0, 1, 3 and f(x): 5, 1, 0, 5. Find f(0) and every x with f(x) = 5.
Equation: f(0) = 1, and f(x) = 5 when x = -2 or x = 3
Testing points on a graph
For f(x) = 2x - 3, are the points (4, 5) and (1, 1) on the graph of f?
Equation: f(4) = 5, so (4, 5) is on the graph. f(1) = -1 ≠ 1, so (1, 1) is not
An equation that does not define a function
Does the equation x = y² define y as a function of x?
Equation: No: x = 4 gives y = 2 and y = -2, so the vertical line x = 4 meets the graph twice
After the last example, sketch the sideways parabola x = y² and draw the vertical line x = 4: it meets the curve at (4, 2) and (4, -2). Compare it with the right side of Diagram 1, where the input 4 sends two arrows. Then use Diagram 2 to model how to read an output from a graph: start at the input on the x-axis, move vertically to the graph, then horizontally to the y-axis.
Guided Practice15 minutes
Pairs work through four relations, one representation each. For each, they write "function" or "not a function" and a one-sentence reason that uses the words input and output: (1) the pairs {(-4, 0), (0, 0), (4, 0)} (a function: every input goes to 0, so the range is {0}); (2) a table with x-values 1, 1, 2, 3 and y-values 5, 6, 7, 8 (not a function: the input 1 has outputs 5 and 6); (3) a mapping from the students in the room to their homeroom teachers (a function, since each student has one homeroom); (4) the graph of the circle with center (0, 0) and radius 5 (not a function: the vertical line x = 3 meets it at (3, 4) and (3, -4)). Then ask pairs to name the domain of relation (1). Listen for students who reject relation (1) because all its outputs are equal; correct that confusion now, using the warm-up machine.
Independent Practice10-15 minutes
Students work alone on five items: (1) state the domain and range of {(-1, 8), (2, 8), (6, -3)} (domain {-1, 2, 6}, range {-3, 8}); (2) a function r has the table x: 0, 2, 4, 6 and r(x): 9, 7, 5, 3; find r(4) (it is 5) and explain in words what r(6) = 3 says; (3) for f(x) = x + 6, decide whether (-2, 4) and (3, 10) lie on the graph ((-2, 4) does, since f(-2) = 4; (3, 10) does not, since f(3) = 9); (4) explain why y² = x + 1 does not define y as a function of x (x = 3 gives y = 2 and y = -2); (5) write your own set of four ordered pairs that is not a function, and trade with a neighbor to check.
Closure5 minutes
Exit ticket: (1) Complete the sentence "A relation is a function when ...". (2) The graph of g contains the point (7, -2). What is g(7)? (Answer: -2.) (3) A classmate says {(3, 1), (4, 1), (5, 1)} is not a function because every output is 1. Write a two-sentence reply.
Differentiation Strategies
For Struggling Students
Have students turn every relation into a mapping diagram before deciding, and circle any input that sends more than one arrow
Give a sentence frame for justifications: "The input ___ is paired with ___ and ___, so ..." or "Every input has one output, so ..."
Use a transparent ruler held vertically and slid across a graph as a physical vertical line test, then connect it to the pairs (a, f(a))
For Advanced Students
Ask students to find a rule from the set {1, 2, 3} to the set {a, b} that is a function whose range uses both letters, and to count how many functions from {1, 2, 3} to {a, b} exist (8)
Ask students to decide whether "each person to their biological mother" and "each person to their sibling" are functions, and to explain what would have to change for the second to become one
Ask students to explain why a horizontal line meeting a graph twice does not stop it from being a function, and what that property would tell them instead
Assessment Guidance
What to Look For
Listen for justifications that name a specific input: "the input 2 is paired with 3 and -1" shows understanding, while "the numbers repeat" does not. Check that students accept repeated outputs and reject repeated inputs with different outputs. When students test a point such as (1, 1) against a formula, look for them to compute f(1) and compare it with the y-coordinate, rather than substituting into the formula in an unclear way. Students who can say why the vertical line test works (each vertical line x = a contains the points with input a) have linked the graph to the definition.
02
Classroom Activities
3 Activities
1
Function or Not? Card Sort
20 minPairs
Pairs sort 12 cards into "function" and "not a function" piles. The cards use every representation in the lesson, so students must apply the same definition to ordered pairs, tables, mappings, graphs, equations and verbal rules.
The 12 Cards (answers for the teacher)
Card 1: {(0, 3), (1, 4), (2, 5)}: function
Card 2: {(5, 2), (5, 8), (6, 1)}: not a function (input 5)
Card 3: table with x: -1, 0, 1, 2 and y: 1, 1, 1, 1: function
Card 4: table with x: 3, 3, 4, 5 and y: 0, 2, 4, 6: not a function (input 3)
Card 5: each US state to its capital city: function
Card 6: each first name to a student in the school with that name: not a function when two students share a name
Card 7: graph of the horizontal line y = -2: function
Card 8: graph of the vertical line x = 1: not a function
Card 9: graph of the parabola y = x² - 1: function
Card 10: the equation y = 7 - 3x: function
Card 11: the equation x² + y² = 16: not a function (x = 0 gives y = 4 and y = -4)
Card 12: each day of September to the high temperature in your town that day: function
Procedure
Pairs sort the cards and write a one-line reason on the back of each card
For every "not a function" card, pairs must name a specific input with two outputs
Pairs join another pair, compare piles and resolve any disagreement using the definition
Discussion Questions
Card 3 has the same output four times. Why is it still a function?
Card 6 depends on the school. What would make it a function?
What do the graph cards that fail have in common?
2
Human Mapping Diagram
15 minGroups of 5-6
Students become the domain. Each group builds a physical mapping diagram on the wall with yarn and index cards and tests three rules against the definition, including one rule that fails because an input has no output.
Setup
Tape 12 index cards labeled January to December on the wall: this is the range side
Each group member writes their first name on an index card: this is the domain side
Give each group several lengths of yarn and masking tape for the arrows
Procedure
Rule 1: person to birth month. Each student tapes one piece of yarn from their name to their month. Ask: is this a function? (Yes, even if two people share a month.)
Rule 2: month to a person born in that month. Now the months are the domain. Ask: what happens to a month with nobody, or with two people? (It fails the definition in two ways: some inputs have no output, some have two.)
Rule 3: person to number of siblings. Groups decide and write the domain and range as sets
Modification for Distance Learning
Use a shared slide with name boxes and month boxes. Students draw their own arrows with the line tool, and the class decides together which rules are functions.
3
From Table to Graph and Back
20 minPairs
Pairs build the graph of f(x) = 4 - x² from a table of pairs (x, f(x)), then use the rule "(a, b) is on the graph exactly when f(a) = b" to test points and to read outputs back from the graph.
Procedure
Complete the table for x = -3, -2, -1, 0, 1, 2, 3. (Outputs: -5, 0, 3, 4, 3, 0, -5.)
Plot the seven points (x, f(x)) on graph paper and join them with a smooth curve: this is the graph of y = 4 - x²
Test four point cards by computing f of the x-coordinate: (1, 3) is on the graph, (2, 1) is not because f(2) = 0, (-3, -5) is on the graph, (0, 3) is not because f(0) = 4
Find every a for which (a, 0) is on the graph, and write the answer in function notation (f(2) = 0 and f(-2) = 0)
Discussion Questions
Why is testing a point with the formula the same as checking the graph?
Slide a ruler held vertically across your graph. Why can it never cross the curve twice?
Two x-values give the output 3. Does that break the definition of a function?
Challenge Variation
Give pairs only the graph of a different function with no formula. Ask them to write five true statements of the form f(a) = b read from the graph, and one statement that is false, for another pair to find.
03
Diagrams & Visual Aids
2 diagrams
Diagram 1: Mapping Diagrams for a Function and a Non-Function
Left: f(x) = x² on the domain {-2, -1, 1, 2}. Each input sends exactly one arrow, even though two inputs share the output 1 and two share the output 4, so f is a function with range {1, 4}. Right: the relation x = y² on the inputs {0, 1, 4}. The inputs 1 and 4 each send two arrows (red), so y is not a function of x.
Diagram 2: Reading f(x) from the Graph of y = f(x)
Graph of f(x) = x² - 4x + 5 for -0.5 ≤ x ≤ 4.5, drawn to scale. The dashed path shows how to read f(4) = 5. The point (1, 2) is on the graph because f(1) = 2; the open point (1, 4) is not. Every point on the curve has the form (x, f(x)).
04
Homework Assignment
~30 min
HSF.IF.A.1 Homework: Functions, Domain, Range and Graphs
Directions: Show your reasoning. Whenever you say a relation is not a function, name a specific input and its two outputs. Write domains and ranges as sets in braces.
Part 1: Is It a Function? (Problems 1-2)
Decide whether each relation is a function. If it is, give its domain and range. (a) {(-3, 2), (0, 2), (4, 2)} (b) {(5, 1), (7, 3), (5, -1)} (c) the table with x: 1, 2, 3, 4 and y: 10, 20, 10, 40
Decide whether each rule is a function and explain. (a) Each student in your math class to their student ID number. (b) Each whole number of people n from 1 to 6 to the total cost, in dollars, of n movie tickets at $9 each; give the domain and range. (c) Each height in centimeters to a student in your class with that height.
Part 2: Function Notation (Problems 3-4)
A function g has the table x: -1, 0, 2, 5, 6 and g(x): 3, -2, 3, 0, 8. (a) Find g(2) and g(5). (b) Find every x with g(x) = 3. (c) Explain why g(3) has no value for this function. (d) Explain the difference between g(0) and the equation g(x) = 0, and give the answer to each.
Let h(x) = 5 - 2x. (a) In words, what does h(3) stand for? Find h(3) and h(-4). (b) The point (k, 9) is on the graph of h. Find k and explain how you know.
Part 3: Graphs of Functions (Problems 5-6)
Let f(x) = x² - 3. Decide whether each point is on the graph of f by computing f of its x-coordinate: (2, 1), (-2, 1), (0, 3), (-1, -2). Then explain why the graph of f cannot contain both (1, -2) and (1, 5).
For each equation, decide whether it defines y as a function of x. For each one that does not, give an x-value that has two or more y-values. (a) y = 3x + 1 (b) x² + y² = 36 (c) y = |x| (d) x = 2
Rubric
Criterion
Full Credit (2 pts)
Partial Credit (1 pt)
No Credit (0 pts)
Function Decisions
Every decision correct with a specific input named
Decisions correct, reasons vague
Decisions mostly incorrect
Domain and Range
All sets correct, no repeated elements
One set incorrect or incomplete
Sets missing or swapped
Function Notation
Values and meanings of g(x) and h(x) correct
Values correct, explanations incomplete
Notation read as multiplication or missing
Graphs
Points tested by computing f(a) and compared correctly
Most points correct
No reasoning shown
05
Quiz: 20 Questions
Interactive, with answers
Instructions
Answer each question, then open the explanation to check your reasoning. Your score updates as you go, and Reset quiz clears every answer so the class can try again.
Multiple choice: pick an option to check it. Short answer: write your answer, then reveal the model answer.
0 of 20 answered · 0 correct
Question 1 of 20 · Multiple Choice
Which set of ordered pairs is a function?
Answer: B
In choice B each input 0, 1 and 2 appears once, so each has exactly one output; sharing the output 5 is allowed. Choices A, C and D each repeat an input with a different output (1, 3 and -1). A student who rejects B because "the outputs repeat" has the definition backwards.
Question 2 of 20 · Multiple Choice
The relation {(4, -1), (6, 2), (9, -1), (6, 0)} is not a function. Why?
Answer: D
A function assigns each input exactly one output, and the input 6 has two outputs. Choice A describes something functions are allowed to do: 4 and 9 may share the output -1.
Question 3 of 20 · Multiple Choice
What is the domain of {(-2, 7), (0, 3), (5, 7), (8, 1)}?
Answer: C
The domain is the set of inputs, the first coordinates: {-2, 0, 5, 8}. Choice A is the range (the outputs). Choice B mixes inputs and outputs. Choice D lists only the smallest and largest inputs.
Question 4 of 20 · Multiple Choice
What is the range of {(3, -4), (-1, 6), (2, -4), (7, 0)}?
Answer: A
The range is the set of outputs: -4, 6, -4, 0. A set lists -4 only once, so the range is {-4, 0, 6}. Choice B is the domain. Choice C leaves out the output 0.
Question 5 of 20 · Multiple Choice
Which statement is true of every function?
Answer: C
This is the definition in HSF.IF.A.1. Choices A and B describe a one-to-one function, which is a special case: f(x) = x² sends both 2 and -2 to 4 and is still a function. Choice D fails for {(1, 5), (2, 5)}, which has two inputs and one output.
Question 6 of 20 · Multiple Choice
A function f has the table x: 1, 2, 3, 4 and f(x): 6, -2, 6, 0. What is f(3)?
Answer: D
f(3) is the output paired with the input 3, which is 6. Choice A assumes the output equals the input. Choice B reads the output for x = 2, and choice C reads the output for x = 4.
Question 7 of 20 · Multiple Choice
For the same table (x: 1, 2, 3, 4 and f(x): 6, -2, 6, 0), which x-values give f(x) = 6?
Answer: A
Look for 6 in the output row: it appears for the inputs 1 and 3. Choice B confuses the output 6 with an input; 6 is not in the domain. Choice C stops after one match.
Question 8 of 20 · Multiple Choice
Which point lies on the graph of f(x) = 4x - 7?
Answer: B
f(3) = 12 - 7 = 5, so (3, 5) is on the graph. Choice A swaps the coordinates: f(5) = 13, not 3. Choice C drops the negative sign: f(0) = -7. Choice D uses f(2) = 1, not -1.
Question 9 of 20 · Multiple Choice
The point (-2, 9) lies on the graph of a function g. Which statement must be true?
Answer: A
A point (a, b) is on the graph of g exactly when g(a) = b, so g(-2) = 9. Choice B reverses the input and the output. Choice C reads g(-2) as multiplication. Choice D generalizes from a single point.
Question 10 of 20 · Multiple Choice
Which equation does not define y as a function of x?
Answer: D
In x = |y|, the input x = 3 gives y = 3 and y = -3, so the vertical line x = 3 meets the graph twice. Choices A, B and C each give one y for every x; choice A is a common trap because x² makes students think of two values, but two x-values sharing one y-value is allowed.
Question 11 of 20 · Multiple Choice
What does the statement f(5) = 12 mean?
Answer: C
f(5) names the output that f assigns to the input 5, and the statement says that output is 12. Choice A reads the notation as multiplication. Choice B swaps input and output. Choice D confuses one input-output pair with the whole domain.
Question 12 of 20 · Multiple Choice
Rule A assigns each student in a school to the one locker they were given. Rule B assigns each locker color (red, blue or gray) to the students with a locker of that color. Which rules are functions?
Answer: B
Rule A gives each student exactly one locker, so it is a function. Rule B sends one color to many students, so an input has more than one output. Choosing A (both) treats "a rule that makes sense" as a function without checking the "exactly one" condition.
Question 13 of 20 · Multiple Choice
The graph of a function f passes through (0, -1), (1, 2) and (3, 8). Which rule could define f?
Answer: A
Check every point: 3(0) - 1 = -1, 3(1) - 1 = 2 and 3(3) - 1 = 8. Each wrong choice fits only one point: x - 1 fits (0, -1), 2x and x² + 1 fit (1, 2). Checking a single point is not enough to identify the rule.
Question 14 of 20 · Multiple Choice
Let f(x) = x² - 2x. How many points on the graph of f have x-coordinate 3?
Answer: C
Because f is a function, the input 3 has exactly one output: f(3) = 9 - 6 = 3, so the only point is (3, 3). Choice B pictures two outputs for one input, which a function never has. Choice D computes 9 + 6 instead of 9 - 6.
Question 15 of 20 · Short Answer
Is {(2, 8), (-5, 8), (0, 1), (2, 8)} a function? Give its domain and range.
Yes, it is a function. The pair (2, 8) is listed twice, but the input 2 still has only one output, 8. Domain {-5, 0, 2}, range {1, 8}. A common error is to reject it because 2 appears twice; what matters is whether an input has two different outputs.
Question 16 of 20 · Short Answer
Let k(x) = 10 - x². Find k(-3) and name the point on the graph of k with x-coordinate -3.
k(-3) = 10 - (-3)² = 10 - 9 = 1, so the point is (-3, 1). A common error is computing -3² as -9, which gives 19.
Question 17 of 20 · Short Answer
A relation contains the pairs (7, 2) and (7, -2). Explain why it is not a function, and describe what its graph shows.
The input 7 is assigned two different outputs, 2 and -2, which breaks the "exactly one" condition. On a graph, both points lie on the vertical line x = 7, so that vertical line meets the graph twice.
Question 18 of 20 · Short Answer
A function p has the table x: 0, 1, 2, 3 and p(x): 5, 5, 5, 5. Is p a function? State its domain and range.
Yes. Each input has exactly one output. Domain {0, 1, 2, 3}, range {5}. Its graph is four points on the horizontal line y = 5, and a constant function is still a function.
Question 19 of 20 · Short Answer
Does the point (-1, 4) lie on the graph of f(x) = 2x² + 3x + 5? Show how you decide.
Compute f(-1) = 2(1) + 3(-1) + 5 = 2 - 3 + 5 = 4. Since f(-1) = 4, yes, (-1, 4) is on the graph. The test is always the same: evaluate f at the x-coordinate and compare with the y-coordinate.
Question 20 of 20 · Short Answer
A parking garage bills only whole hours, at $3 per hour, for stays of 0 to 8 hours. The function P assigns each number of hours h in {0, 1, 2, ..., 8} the fee P(h) in dollars. Find P(5), state the range of P, and explain why P(2.5) has no value for this function.
P(5) = 3 · 5 = 15: a 5-hour stay costs $15. The range is {0, 3, 6, 9, 12, 15, 18, 21, 24}. P(2.5) has no value because 2.5 is not in the domain: the function is only defined for whole numbers of hours from 0 to 8.
0 of 20 answered · 0 correct
06
Frequently Asked Questions
10 Questions
What does HSF.IF.A.1 mean?
It means students understand the definition of a function and its notation. A function assigns each input in its domain exactly one output in its range; f(x) names the output for the input x; and the graph of f is the set of points (x, y) where y = f(x). The standard is about understanding, so students should be able to explain why a relation is or is not a function, not only recite a test.
Is HSF.IF.A.1 taught in Algebra 1 or Algebra 2?
It is usually taught at the start of the functions unit in Algebra I. Students meet the informal idea in grade 8 (8.F.A.1), and HSF.IF.A.1 adds the words domain and range and the notation f(x). Algebra II and Precalculus reuse the definition constantly, for example when they restrict domains or work with inverse functions.
Can two different inputs have the same output?
Yes. The definition only limits how many outputs each input has, not how many inputs share an output. f(x) = x² sends both 3 and -3 to 9 and is a function. What is not allowed is one input with two different outputs, such as (2, 3) and (2, -1) in the same relation.
Why does the vertical line test work?
Because the graph of f is the graph of y = f(x). The vertical line x = a contains every point whose input is a. If the line crosses the graph twice, the input a has two outputs, so the graph cannot belong to a function. Teach the test as a consequence of the definition, so students can explain it instead of only applying it.
Does f(x) mean f times x?
No. f(x) is read "f of x" and names the output of the function f for the input x. The parentheses mark the input, not multiplication. A quick classroom check is to ask what f(3) means for a table: students should point to the output in the column for 3, not multiply anything.
What is the difference between range and codomain?
The standard calls the target set the range. Many college texts split this into the codomain (the set the outputs are allowed to come from) and the range (the outputs that actually occur). In Algebra I, "range" usually means the set of outputs that actually occur, which is how this lesson uses it. For {(1, 4), (2, 7), (3, 4)} the range is {4, 7}.
Is every equation in x and y a function?
No. An equation defines y as a function of x only if each x-value gives exactly one y-value. y = 3x - 5 and y = x² do; x² + y² = 25 and x = y² do not, because, for example, x = 3 in the circle gives y = 4 and y = -4. Solving for y and seeing a ± sign is a quick warning sign.
What mistakes do students make with domain and range?
A common one is swapping them: the domain is the set of inputs (first coordinates), the range the set of outputs (second coordinates). Other frequent slips are listing repeated outputs twice in the range, and rejecting a relation as a function because an output repeats. Asking students to say "input" and "output" aloud with each set helps.
How is HSF.IF.A.1 different from 8.F.A.1?
In grade 8, a function is introduced informally as a rule that gives each input one output, with graphs as sets of ordered pairs. HSF.IF.A.1 formalizes the same idea with the named sets domain and range and with function notation f(x), and it states precisely that the graph of f is the graph of y = f(x). High school students are expected to use the vocabulary and notation fluently.
How is this standard tested?
Directly, with items that ask whether a table, mapping, set of pairs or graph represents a function, and items that ask for the domain or range of a finite relation. Indirectly, function notation and reading points from graphs appear in many later items, including the Advanced Math domain of the digital SAT. Students who can justify their answers in words tend to handle the unfamiliar formats best.
07
Related Standards
5 standards
These standards connect to HSF.IF.A.1: prerequisites to review first, parallel standards at the same level, and next steps that build on it.
Before this lesson
8.F.A.1Prerequisite
Understand a function as a rule assigning each input exactly one output
