HSF.LE.A.2: Constructing Linear and Exponential Functions
In plain English: HSF.LE.A.2 is the Common Core functions standard that asks students to write linear and exponential functions, including arithmetic and geometric sequences, from a graph, a verbal description or two input-output pairs, such as two rows of a table. The key idea is that a constant difference gives a linear rule and a constant ratio gives an exponential rule. It is usually taught in Algebra I.
Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).
Common Core State Standards for Mathematics · Domain: Linear, Quadratic, and Exponential Models (LE) · Cluster: Construct and compare linear, quadratic, and exponential models and solve problems Also written as HSF-LE.A.2 or F-LE.2 · Official standard
Students write linear and exponential functions, including arithmetic and geometric sequences, from each kind of information the standard names: a graph, a description of a relationship, and two input-output pairs, including pairs read from a table. The unifying idea is short: a constant difference gives a linear rule, and a constant ratio gives an exponential rule.
The lesson treats sequences as functions on the whole numbers, so an = a1 + d(n - 1) is a linear function of n and an = a1 · rn - 1 is an exponential one. Students practice choosing the model, solving for its two parameters, and checking the rule against a third value.
Learning Objectives
By the end of this lesson, students will be able to:
Write a linear function or an arithmetic sequence given two input-output pairs, a table, a graph or a description
Write an exponential function or a geometric sequence given two input-output pairs, a table, a graph or a description
Decide from the information given whether the relationship has a constant difference or a constant ratio
Check a constructed function by substituting a value that was not used to build it
Prior Knowledge Required
Students should already be comfortable with:
Finding the rate of change and initial value of a linear function from two points, a table or a graph 8.F.B.4
Telling linear and exponential situations apart by differences and factors HSF.LE.A.1
Sequences as functions whose domain is a subset of the integers HSF.IF.A.3
Square roots and cube roots of whole numbers and simple fractions 8.EE.A.2
Write two patterns on the board and ask students to work alone for three minutes.
Warm-Up Prompt
"Pattern 1: 7, 11, 15, 19, ... Pattern 2: 3, 12, 48, 192, ... Find the next two terms of each. Then describe how you could find the 20th term of each pattern without writing out all 20 terms."
Collect answers: 23 and 27 for Pattern 1, and 768 and 3,072 for Pattern 2. Students usually describe Pattern 1 as "start at 7 and add 4 nineteen times," which gives 7 + 4 · 19 = 83. For Pattern 2, "start at 3 and multiply by 4 nineteen times" gives 3 · 419. Ask why the count is 19 and not 20: the first term already exists before any step is taken. Tell students that today they will write rules like these from any starting information: a description, a graph, a table or just two points.
Direct Instruction25 minutes
Four function types, three kinds of information. Linear functions and arithmetic sequences change by a constant difference; exponential functions and geometric sequences change by a constant ratio. A sequence is a function whose inputs are the term numbers n = 1, 2, 3, and so on. Show the four rules side by side: f(x) = mx + b, g(x) = a · bx, an = a1 + d(n - 1) and an = a1 · rn - 1. Then model a method for each kind of starting information:
Two input-output pairs, linear: slope m = (y2 - y1) ÷ (x2 - x1), then solve y1 = m x1 + b for b.
Two input-output pairs, exponential: divide the outputs, y2 ÷ y1 = bx2 - x1, and take the root to find b. Then a = y1 ÷ bx1.
A table: pick two rows and use the steps above, then check a third row. Test differences first; if they are not constant, test ratios.
A graph: read two points where the graph crosses grid intersections exactly, preferably the y-intercept, which gives b or a directly.
A description: find the starting value and whether the change is an amount (difference) or a multiplier (ratio) per unit.
Work the linear graph in Diagram 1 first: the line passes through (0, -3) and (3, 3), so the rise is 6 over a run of 3, m = 2 and f(x) = 2x - 3. Then work the examples below. In each one, ask students which of the four types it is before they compute anything.
Linear, from two input-output pairs
Write the linear function through (2, 11) and (6, 23).
Equation: m = (23 - 11) ÷ (6 - 2) = 3, b = 11 - 3 · 2 = 5, so f(x) = 3x + 5
Exponential, from two input-output pairs
Write y = a · bˣ through (1, 12) and (3, 108).
Equation: b² = 108 ÷ 12 = 9, so b = 3 and a = 12 ÷ 3 = 4: y = 4 · 3ˣ
Arithmetic sequence, from a description
A theater has 18 seats in row 1, and each row has 4 more seats than the row in front of it.
Equation: aₙ = 18 + 4(n - 1) = 4n + 14, so row 25 has 114 seats
Geometric sequence, from a table
A table lists n = 1, 2, 3, 4 and aₙ = 2, 10, 50, 250.
Equation: r = 10 ÷ 2 = 5, so aₙ = 2 · 5ⁿ⁻¹
Exponential, from a graph
The graph in Diagram 1 passes through the grid points (0, 80) and (2, 20).
Equation: a = 80, b² = 20 ÷ 80 = 1/4, so b = 1/2: y = 80(1/2)ˣ
After Example 4, point out that for a geometric sequence, knowing two terms that are two places apart gives r2, and both r and -r fit. Context or a positive-terms condition decides which one to keep.
Guided Practice15 minutes
Pairs write a rule for each item, then check it by substituting a value not used to build it.
Table: x = 0, 1, 2, 3 and y = 7, 9.5, 12, 14.5 (linear: y = 2.5x + 7)
Two pairs: (0, 400) and (1, 300), exponential (y = 400(0.75)x)
Description: a bike rental costs $8 plus $3.50 per hour (C = 3.5h + 8)
Description: a ball dropped from a height rebounds to 150 cm on the first bounce, and each rebound reaches 60% of the height of the one before (geometric: hn = 150(0.6)n - 1, so the third rebound reaches 54 cm)
Circulate and ask, "Is the change an amount or a multiplier?" Watch for students who write 0.6 · 150n - 1 (base and coefficient switched) or who use n instead of n - 1.
Independent Practice15 minutes
Students write each function on their own and check one extra value.
The linear function through (3, 14) and (7, 34) (y = 5x - 1)
The exponential function through (0, 6) and (2, 54) (y = 6 · 3x)
The arithmetic sequence with a4 = 25 and a10 = 61 (d = 6, an = 6n + 1)
The geometric sequence with a2 = 12 and a5 = 324 (r = 3, an = 4 · 3n - 1)
$500 deposited at 3% interest compounded yearly (B = 500(1.03)t)
A line on a graph through the grid points (0, 10) and (5, 0) (y = -2x + 10)
Closure5-10 minutes
Exit ticket: (1) Write the exponential function through (1, 10) and (2, 25). (b = 2.5 and a = 4, so y = 4(2.5)x.) (2) Write an explicit rule for the arithmetic sequence -3, 2, 7, 12, ... (an = 5n - 8.) (3) In one sentence, explain how you decide between a linear and an exponential rule when you are given a table.
Differentiation Strategies
For Struggling Students
Give a decision card: "Subtract two outputs. Same each time? Linear. If not, divide. Same each time? Exponential."
Start with pairs that include the y-intercept, such as (0, 6), so a or b is known before any solving
Have students list the first four terms of a sequence before writing the explicit rule, and check the rule on n = 1
For Advanced Students
Give two points with x-values 3 apart, such as (1, 5) and (4, 40), and have students find b with a cube root
Ask for a geometric sequence with a2 = 6 and a4 = 24 that has alternating signs, and explain why two sequences fit
Ask students to write the same arithmetic sequence as a function of n starting at n = 0 and starting at n = 1, and explain how the rules differ
Assessment Guidance
What to Look For
Check that students choose the model from the evidence (a constant difference or a constant ratio) before computing, and that they can explain the choice. For exponential rules, look for the division step y2 ÷ y1 = bx2 - x1 and for a found as y1 ÷ bx1, not as y1 itself. For sequences, make sure the first term gives n = 1 in the rule. Every answer should include a check with a third value.
02
Classroom Activities
3 Activities
1
Two Points, Two Models
20 minPairs
Each pair gets three sets of two points. For each set, they build both the linear function and the exponential function through the points, graph both, and see how differently they continue.
Point Sets
Set 1: (0, 4) and (2, 36). Linear: y = 16x + 4. Exponential: y = 4 · 3x
Set 2: (1, 6) and (3, 24). Linear: y = 9x - 3. Exponential: y = 3 · 2x
Set 3: (0, 250) and (3, 16). Linear: y = -78x + 250. Exponential: y = 250(0.4)x
Procedure
Partner A builds the linear function and Partner B the exponential function; they swap roles for each set
Both partners graph the two functions on the same grid and mark the two given points
Pairs predict each function's value at x = 4, then compute it. For Set 1: 68 and 324. For Set 3: -62 and 6.4
Discussion Questions
Two points always determine one line. Why do they also determine one exponential function y = a · bx (with both outputs positive)?
In Set 3, which model could describe a quantity that cannot be negative? Why?
What extra information would tell you which model is correct for real data?
2
Sequence Stations
25 minGroups of 3-4
Four stations each give one arithmetic or geometric sequence in a different form. Groups rotate every 5 minutes, write an explicit rule and find the 10th term.
The 4 Stations
Station A (description): a stack of plastic cups. One cup is 12 cm tall and each added cup adds 1.5 cm. Rule: hn = 12 + 1.5(n - 1) = 1.5n + 10.5; h10 = 25.5 cm
Station B (table): n = 1, 2, 3, 4 and an = 640, 160, 40, 10. Rule: an = 640(1/4)n - 1; a10 = 640 ÷ 49 = 5/2048
Station C (graph): a dot graph with points (1, 3), (2, 7), (3, 11) and (4, 15). Rule: an = 4n - 1; a10 = 39
Station D (two terms): a geometric sequence with a3 = 18 and a5 = 162. Rule: r2 = 9, so r = 3 or r = -3; an = 2 · 3n - 1 or an = 2(-3)n - 1; a10 = 39,366 or -39,366
Procedure
Each group records, at every station, the type (arithmetic or geometric), the evidence for it, the rule and the 10th term
At the end, groups compare answers for Station D, where two rules fit, and decide what extra fact would pick one
Modification for Distance Learning
Post each station on its own slide in a shared deck. Groups work in breakout rooms and type their rule and evidence on a shared answer slide before moving on.
3
Build It from a Story
15 minPairs
Each pair gets 6 description cards. Partners take turns writing a function for a card while the other partner checks it with a second value from the story.
The 6 Cards
A 3D printer spool holds 1,000 g of filament, and each print uses 18 g: F(p) = 1000 - 18p
An online video had 2,400 views on day 0, and views tripled each day for the first week: V(d) = 2400 · 3d
A tile pattern uses 6 tiles in Figure 1 and 4 more tiles in each new figure: tn = 4n + 2
A tennis tournament starts with 128 players, and half are eliminated each round: players in round n = 128(1/2)n - 1
A car bought for $28,000 loses 12% of its value each year: V(t) = 28000(0.88)t
A parking garage charges $4 for the first hour and $2.50 for each additional hour: cost for n hours = 4 + 2.5(n - 1) = 2.5n + 1.5
Challenge Variation
Pairs write one new card of each type (linear, exponential, arithmetic, geometric) and trade with another pair. The other pair must write the rule and state which part of the description gave each parameter.
03
Diagrams & Visual Aids
2 diagrams
Diagram 1: Reading a Linear and an Exponential Function from a Graph
Both graphs are drawn to scale. Left: the line through (0, -3) and (3, 3) rises 6 over a run of 3, so f(x) = 2x - 3. Right: the curve through (0, 80) and (2, 20) starts at a = 80, and every step of 1 unit to the right halves the output, so y = 80(1/2)x. In both cases the y-intercept gives one parameter directly.
Diagram 2: Graphs for Homework Problem 3
Two graphs drawn to scale for Homework Problem 3. Graph A is a line; Graph B is an exponential curve of the form y = a · bx. Read the marked points and write each function.
04
Homework Assignment
~30 min
HSF.LE.A.2 Homework: Writing Linear and Exponential Functions
Directions: Show all work. For every function or sequence you write, state whether it is linear, exponential, arithmetic or geometric, give your evidence, and check the rule with one value you did not use to build it.
Part 1: Two Points and Tables (Problems 1-2)
(a) Write the linear function whose graph passes through (-2, 9) and (4, -6). (b) Write the exponential function y = a · bx that passes through (1, 18) and (3, 8).
Decide whether each table is linear or exponential and write the function. Table 1: x = 0, 1, 2, 3, 4 and y = 2000, 2100, 2205, 2315.25, 2431.0125. Table 2: x = 2, 4, 6, 8 and y = 19, 31, 43, 55.
Part 2: Graphs and Descriptions (Problems 3-4)
Use Diagram 2. (a) Write the equation of the line in Graph A. (b) Write the exponential function in Graph B. (c) For each graph, find the output at x = 6.
Write a function for each description and use it to answer the question. (a) A pool holds 18,000 gallons and is drained at 450 gallons per hour. How much water is left after 8 hours, and when is the pool empty? (b) A painting bought for $3,500 increases in value by 6% per year. What is it worth after 10 years, to the nearest dollar?
Part 3: Sequences (Problems 5-6)
An arithmetic sequence has a5 = 34 and a12 = 76. Write an explicit rule and find a30.
On day 1, 5 people start sharing a message online. Each day, the number of new people who receive it is 3 times the number from the day before. (a) Explain why the daily numbers form a geometric sequence. (b) Write an explicit rule for the number of new people on day n. (c) How many new people receive it on day 6? (d) Why does r = -3 make no sense here?
Rubric
Criterion
Full Credit (2 pts)
Partial Credit (1 pt)
No Credit (0 pts)
Choice of Model
Type chosen from a constant difference or ratio, with evidence
Correct type without evidence
Wrong type
Parameters
Both parameters correct, found by a clear method
One parameter correct
Neither parameter correct
Sequences
Rules use n - 1 correctly and give the right terms
Rule off by one term
Rule missing or incorrect
Checking and Context
Rule checked with an extra value; answers interpreted in context
Check or interpretation missing
Neither shown
05
Quiz: 20 Questions
Interactive, with answers
Instructions
Choose or write an answer, then open the explanation. The score at the top counts your correct multiple-choice answers, and Reset quiz starts the quiz over.
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 linear function passes through (1, 4) and (5, 16)?
Answer: B
m = (16 - 4) ÷ (5 - 1) = 3, and 4 = 3(1) + b gives b = 1, so y = 3x + 1. Check: 3(5) + 1 = 16. Choice C uses the first output 4 as the y-intercept, but the point (1, 4) is not on the y-axis. Choice D uses the change in y, 12, as the slope without dividing by the change in x.
Question 2 of 20 · Multiple Choice
Which exponential function passes through (0, 7) and (1, 21)?
Answer: C
At x = 0 the output is a, so a = 7. From x = 0 to x = 1 the output is multiplied by 21 ÷ 7 = 3, so b = 3: y = 7 · 3x. Choice A switches a and b. Choice B is the linear function through the same points. Choice D uses the second output as a.
Question 3 of 20 · Multiple Choice
Which exponential function passes through (2, 36) and (3, 108)?
Answer: D
b = 108 ÷ 36 = 3, and a = 36 ÷ 32 = 4, so y = 4 · 3x. Check: 4 · 27 = 108. Choice A takes 36 as a, but 36 is the output at x = 2, not at x = 0. Choice B divides 36 by b only once. Choice C is the line through the two points.
Question 4 of 20 · Multiple Choice
Which explicit rule gives the arithmetic sequence 8, 13, 18, 23, ...?
Answer: A
The common difference is 5, so an = 8 + 5(n - 1) = 5n + 3. Check: a1 = 8 and a4 = 23. Choice B uses n instead of n - 1 and gives 13 as the first term. Choice C treats the difference as a ratio.
Question 5 of 20 · Multiple Choice
Which explicit rule gives the geometric sequence 96, 48, 24, 12, ...?
Answer: C
The common ratio is 48 ÷ 96 = 1/2 and a1 = 96, so an = 96(1/2)n - 1. Choice A gives 48 as the first term. Choice B is arithmetic and gives 0 as the third term. Choice D uses 2 instead of 1/2, so the terms grow.
Question 6 of 20 · Multiple Choice
A tank holds 300 liters of water and is filled at a constant 25 liters per minute. Which function gives the volume V after t minutes?
Answer: A
The starting amount is 300 and the same 25 liters is added each minute: a constant difference, so V = 300 + 25t. Choice B switches the starting value and the rate. Choices C and D multiply instead of adding, which would describe a percent rate or a factor.
Question 7 of 20 · Multiple Choice
A town of 12,000 people loses 3% of its population each year. Which function models the population P after t years?
Answer: D
Losing 3% each year leaves 97%, so the yearly factor is 0.97: P = 12000(0.97)t. Choice A keeps only 3% each year. Choice B is 3% growth. Choice C loses 3% of the original population every year, which is a linear model and does not match "3% of its population each year."
Question 8 of 20 · Multiple Choice
A table shows x = 0, 2, 4, 6 and y = 5, 20, 80, 320. Which function fits?
Answer: B
The output is multiplied by 4 over every 2 units, so b2 = 4 and b = 2; a = 5 from x = 0. Check: 5 · 26 = 320. Choice A takes the factor over 2 units as the factor per unit, so it gives 80 at x = 2. Choice C is the line through the first two rows only.
Question 9 of 20 · Multiple Choice
A table shows x = 1, 2, 3, 4 and y = 11, 7, 3, -1. Which function fits?
Answer: C
The differences are all -4, so m = -4. From 11 = -4(1) + b, b = 15, so y = -4x + 15. Check: -4(4) + 15 = -1. Choice A uses the output at x = 1 as the y-intercept. Choice D assumes a constant ratio, but 3 ÷ 7 is not 7 ÷ 11.
Question 10 of 20 · Multiple Choice
A line on a graph passes through the grid points (0, 1) and (2, -5). What is its equation?
Answer: A
The y-intercept is 1. From x = 0 to x = 2 the line falls 6, so m = -6 ÷ 2 = -3: y = -3x + 1. Choice B drops the sign of the slope. Choice C divides run by rise. Choice D uses the second point's y-value as the intercept.
Question 11 of 20 · Multiple Choice
The graph of y = a · bx passes through the marked points (0, 5) and (1, 2). What is the function?
Answer: D
At x = 0, a = 5. From x = 0 to x = 1 the output is multiplied by 2 ÷ 5 = 0.4, so y = 5(0.4)x, a decreasing curve. Choice B divides the wrong way (5 ÷ 2), which would make the graph increase. Choice C is the line through the two points.
Question 12 of 20 · Multiple Choice
A geometric sequence with positive terms has a2 = 12 and a4 = 48. Which is its explicit rule?
Answer: A
Two steps multiply by r2 = 48 ÷ 12 = 4, so r = 2 (the terms are positive), and a1 = 12 ÷ 2 = 6. Check: 6 · 23 = 48. Choice B treats a2 as the first term. Choice C uses r2 as the ratio. Choice D is the arithmetic sequence through the same two terms.
Question 13 of 20 · Multiple Choice
An arithmetic sequence has a1 = -4 and common difference 7. What is a15?
Answer: B
a15 = -4 + 7(15 - 1) = -4 + 98 = 94. Choice A uses 7 · 15, adding one difference too many. Choice C forgets the first term. Choice D uses 13 differences instead of 14.
Question 14 of 20 · Multiple Choice
A student writes an = 3 + 4n for the sequence 3, 7, 11, 15, ... What is wrong?
Answer: B
Substituting n = 1 into 3 + 4n gives 7, the second term. The first term needs zero steps, so the rule is an = 3 + 4(n - 1) = 4n - 1. Choice A is what you get if you never test n = 1. Choice D mistakes a constant difference for a constant ratio: 7 ÷ 3 is not 11 ÷ 7.
Question 15 of 20 · Short Answer
Write the exponential function y = a · bx whose graph passes through (1, 6) and (4, 162).
Divide: b3 = 162 ÷ 6 = 27, so b = 3. Then a = 6 ÷ 3 = 2. y = 2 · 3x. Check: 2 · 34 = 162.
Question 16 of 20 · Short Answer
Write the linear function whose graph passes through (-3, 10) and (5, -6).
m = (-6 - 10) ÷ (5 - (-3)) = -16 ÷ 8 = -2. From 10 = -2(-3) + b, b = 4. y = -2x + 4. Check: -2(5) + 4 = -6.
Question 17 of 20 · Short Answer
A music library has 350 songs, and its owner adds 12 songs each week. Write a function for the number of songs S after w weeks, and find S after 20 weeks.
The change is a constant 12 songs per week, so the model is linear: S = 350 + 12w. After 20 weeks, S = 350 + 240 = 590 songs.
Question 18 of 20 · Short Answer
A pendulum swings 80 cm on its first swing, and each swing is 90% as long as the one before. Write an explicit rule for the length of swing n and find the length of the 4th swing.
The ratio between swings is 0.9, so the lengths form a geometric sequence: Ln = 80(0.9)n - 1. The 4th swing is 80(0.9)3 = 80(0.729) = 58.32 cm.
Question 19 of 20 · Short Answer
A table shows x = 0, 1, 2, 3 and y = 64, 48, 36, 27. Write a function for the table.
The differences (-16, -12, -9) are not equal, but the ratios are: 48 ÷ 64 = 36 ÷ 48 = 27 ÷ 36 = 0.75. With a = 64: y = 64(0.75)x, exponential decay of 25% per unit.
Question 20 of 20 · Short Answer
A dot graph shows the terms of an arithmetic sequence at (1, 20), (2, 17), (3, 14) and (4, 11). Write an explicit rule and find which term equals -1.
The common difference is -3 and a1 = 20, so an = 20 - 3(n - 1) = 23 - 3n. Solve 23 - 3n = -1: 3n = 24, so n = 8. The 8th term is -1.
0 of 20 answered · 0 correct
06
Frequently Asked Questions
10 Questions
What does HSF.LE.A.2 mean?
HSF.LE.A.2 means students can write a linear or exponential function, including an arithmetic or geometric sequence, from the information they are given. That information can be a graph, a verbal description of a relationship, or two input-output pairs, which may be read from a table. The standard is about building the rule, not only recognizing its type.
Is HSF.LE.A.2 Algebra 1 or Algebra 2?
It is usually taught in Algebra I. Algebra II courses revisit it with harder exponential cases, such as points whose x-values are several units apart or models that need logarithms to solve, but the core skill of writing both kinds of functions belongs to Algebra I.
How do you write an exponential function from two points?
Divide the outputs to find b, then solve for a. For points (x1, y1) and (x2, y2), y2 ÷ y1 = bx2 - x1, so take the appropriate root. Then a = y1 ÷ bx1. If one point has x = 0, its output is a directly. Always check the rule with the other point.
How is an arithmetic sequence related to a linear function?
An arithmetic sequence is a linear function whose inputs are the term numbers 1, 2, 3, and so on. The common difference d plays the role of the slope. Its graph is a set of separate points on a line, not a connected line. In the same way, a geometric sequence is an exponential function on the term numbers, with the common ratio r as the base.
Why do sequence formulas use n - 1?
Because the first term needs no steps. To reach term n from term 1 you take n - 1 steps, so an = a1 + d(n - 1) or an = a1 · rn - 1. A quick check is to substitute n = 1: the rule must return the first term. Some textbooks start sequences at n = 0 instead, and then the rule uses n.
How do students read a function from a graph?
Choose two points where the graph crosses grid intersections exactly, ideally including the y-intercept. For a line, compute rise over run. For an exponential curve, divide the outputs of points one unit apart to get b. Points that fall between grid lines only give estimates, so they should not be used to build an exact rule.
Can the same two points give both a linear and an exponential function?
Yes. Any two points with different x-values lie on exactly one line, and if both outputs are positive they also lie on exactly one curve y = a · bx. For (1, 6) and (3, 24), the line is y = 9x - 3 and the exponential is y = 3 · 2x. The context or a third data point decides which model fits.
What are common mistakes on HSF.LE.A.2 problems?
Common mistakes are using the first output as the y-intercept when that point is not at x = 0, using the ratio over two units as the ratio per unit, writing the percent as the factor (0.04 instead of 0.96 for a 4% decrease), switching a and b, and using n instead of n - 1 in sequence rules.
How can students tell from a description whether to use a linear or an exponential model?
Ask whether the change is an amount or a multiplier. "Adds 5 books each month" or "cools 2 degrees per hour" is an amount per unit, so the model is linear. "Grows 4% per year," "doubles each day" or "each bounce is 70% of the one before" is a multiplier per unit, so the model is exponential.
How does HSF.LE.A.2 connect to other standards?
It builds on telling linear and exponential situations apart (HSF.LE.A.1) and on seeing sequences as functions (HSF.IF.A.3). It runs alongside writing sequences recursively and explicitly (HSF.BF.A.2), and it leads to interpreting parameters in context (HSF.LE.B.5) and solving exponential equations with logarithms (HSF.LE.A.4).
07
Related Standards
6 standards
These standards connect to HSF.LE.A.2: prerequisites to review first, parallel standards at the same level, and next steps that build on it.
Before this lesson
8.F.B.4Prerequisite
Construct a linear model and find its rate of change and initial value
