Curriculum / Math / 9th Grade / Unit 6: Exponents and Exponential Functions / Lesson 18
Math
Unit 6
9th Grade
Lesson 18 of 22
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Lesson Notes
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Graph exponential growth functions and write exponential growth functions from graphs.
The core standards covered in this lesson
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.
The foundational standards covered in this lesson
8.F.B.4 — Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
25-30 minutes
Consider the geometric sequence below.
$${2,\space6,\space18,\space54,\space162, …}$$
Write a function in the form $${f(x)=a\cdot b^x}$$ for each graph below.
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.
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.
A set of suggested resources or problem types that teachers can turn into a problem set
15-20 minutes
Give your students more opportunities to practice the skills in this lesson with a downloadable problem set aligned to the daily objective.
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
5-10 minutes
Sketch the graph of $${f(x)=2^{(x+3)}+4}$$.
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.
Next
Write exponential growth functions to model financial applications, including compound interest.
Topic A: Exponent Rules, Expressions, and Radicals
Use exponent rules to analyze and rewrite expressions with non-negative exponents.
Standards
8.EE.A.1
Add and subtract polynomial expressions using properties of operations.
A.APR.A.1
Multiply polynomials using properties of exponents and properties of operations.
Solve mathematical applications of exponential expressions.
Use negative exponent rules to analyze and rewrite exponential expressions.
8.EE.A.1A.SSE.A.2
Define rational exponents and convert between rational exponents and roots.
N.RN.A.1N.RN.A.2
Write equivalent radical and rational exponent expressions. Identify quantities as rational or irrational.
N.RN.B.3
Simplify radical expressions.
N.RN.A.2
Multiply and divide rational exponent expressions and radical expressions.
N.RN.A.2N.RN.B.3
Add and subtract rational exponent expressions and radical expressions.
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Topic B: Arithmetic and Geometric Sequences
Describe and analyze sequences given their recursive formulas.
F.BF.A.2F.IF.A.2F.IF.A.3
Write recursive formulas for sequences, including the Fibonacci sequence.
Define arithmetic and geometric sequences, and identify common ratios and common differences in sequences.
F.BF.A.2F.LE.A.2
Write explicit rules for arithmetic sequences and translate between explicit and recursive formulas.
F.BF.A.2F.IF.A.3F.LE.A.2
Write explicit rules for geometric sequences and translate between explicit and recursive formulas.
Topic C: Exponential Growth and Decay
Compare rates of change in linear and exponential functions shown as equations, graphs, and situations.
A.SSE.A.1F.IF.C.9F.LE.A.1F.LE.A.3
Write linear and exponential models for real-world and mathematical problems.
A.SSE.A.1F.LE.A.1F.LE.A.2F.LE.B.5
F.BF.B.3F.IF.C.7.E
F.IF.C.8.BF.LE.A.2F.LE.B.5
Write, graph, and evaluate exponential decay functions.
F.BF.B.3F.IF.C.7.EF.IF.C.8.BF.LE.A.1.C
Identify features of exponential decay in real-world problems.
F.IF.C.8.BF.LE.A.1.C
Solve exponential growth and exponential decay application problems.
F.IF.C.8.BF.LE.A.1F.LE.A.2
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