Exponents and Exponential Functions

Lesson 18

Math

Unit 6

9th Grade

Lesson 18 of 22

Objective


Graph exponential growth functions and write exponential growth functions from graphs.

Common Core Standards


Core Standards

  • F.BF.B.3 — Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.
  • F.IF.C.7.E — Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.

Foundational Standards

  • 8.F.B.4

Criteria for Success


  1. Analyze an exponential growth function in equation form to identify features in the graph of the function including the $$y$$-intercept, domain, range, rate of change, etc.
  2. Analyze the graph of an exponential growth function to write an equation for the function. 
  3. Transform the graph of the parent function $${f(x)=a^x}$$.
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Anchor Problems


Problem 1

Consider the geometric sequence below. 

$${2,\space6,\space18,\space54,\space162, …}$$

  1. Write an explicit function, $${ f(x)}$$, to represent the sequence. In this case, let the first term in the sequence correspond to $${ x=0}$$.
  2. What is the $$y$$-intercept of the graph of the function? 
  3. What coordinate point does each number in the sequence correspond to?
  4. Sketch a graph of the exponential function given by the geometric sequence. 

Guiding Questions

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Problem 2

Write a function in the form $${f(x)=a\cdot b^x}$$ for each graph below.

Guiding Questions

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References

Illustrative Mathematics Identifying Exponential FunctionsPart B

Identifying Exponential Functions, accessed on May 17, 2018, 1:10 p.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.

Modified by Fishtank Learning, Inc.

Problem 3

The graph of the parent function $${{y=2^x}}$$ is shown.

For each function below, describe the transformation to the graph of the parent function $${{y=2^x}}$$. Then sketch the graph.

Guiding Questions

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Problem Set


Give your students more opportunities to practice the skills in this lesson with a downloadable problem set aligned to the daily objective.

Target Task


Sketch the graph of $${f(x)=2^{(x+3)}+4}$$.

Additional Practice


The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.

  • Include examples where students match equations to graphs of exponential functions, and perform error analysis on mismatched equations and graphs
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Lesson 17

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Lesson 19

Lesson Map

A7CB09C2-D12F-4F55-80DB-37298FF0A765

Topic A: Exponent Rules, Expressions, and Radicals

Topic B: Arithmetic and Geometric Sequences

Topic C: Exponential Growth and Decay

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