Writing Exponential Functions

Presentation

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Mathematics

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9th - 12th Grade

•

Medium

•

CCSS

HSF.LE.A.2, HSF-IF.C.7E, HSF-IF.C.8B

Standards-aligned

Erika Foster

Used 371+ times

FREE Resource

10 Slides • 9 Questions

Writing Exponential Functions

The Basics

An exponential function with base b is defined by $f\left(x\right)=ab^x$ where a ≠0, b > 0 , b ≠1, and x is any real number.

The base, b, is constant and the exponent, x, is a variable.

More Basics

If all the x-values have a constant difference and all of the y-values have a constant ratio, then the table represents an Exponential Function.

For example, $f\left(x\right)\ =2^x$ is shown in the table to the right.

Example 1

Does the table or equation represent an exponential function? Explain.

Example 2

Find the equation of the exponential function for the table.

Example 3

Find the equation of the exponential function for the table.

Example 4

Find the equation of the exponential function for the table.

Multiple Choice

What is the y-intercept of the function: $f\left(x\right)=2\left(4\right)^x$ ?

$\left(4\right)^x$

Multiple Choice

What is the y-intercept of the function: $f\left(x\right)=3\left(\frac{1}{2}\right)^x$ ?

$\frac{1}{2}$

$\left(\frac{1}{2}\right)^x$

$\frac{3}{2}$

Multiple Choice

What is the Growth/Decay factor of the function: $f\left(x\right)=2\left(4\right)^x$ ?

Multiple Choice

What is the Growth/Decay factor of the function: $f\left(x\right)=3\left(\frac{1}{2}\right)^x$ ?

$\frac{1}{2}$

$\left(\frac{1}{2}\right)^x$

$\frac{3}{2}$

Multiple Choice

Write the equation of the exponential function for the given table.

$y=3^x$

$y=12\left(3\right)^x$

$y=3\left(4\right)^x$

$y=4\left(3\right)^x$

Multiple Choice

Write the equation of the exponential function for the given table.

$y=-2\left(\frac{1}{2}\right)^x$

$y=2\left(\frac{1}{2}\right)^x$

$y=2\left(2\right)^x$

$y=\frac{1}{2}\left(2\right)^x$

Multiple Choice

Write the equation of the exponential function for the given table.

$y=2\left(\frac{1}{3}\right)^x$

$y=-2\left(\frac{1}{3}\right)^x$

$y=\frac{1}{3}\left(2\right)^x$

$y=2\left(-\frac{1}{3}\right)^x$

Example 5

Write the equation for the graph.

Example 6

Write the equation for the graph.

Example 7

Write the equation for the graph.

Multiple Choice

Write the equation of the exponential function for the given graph.

y = 2(2)^x

y = 2(1)^x

$y=1\left(\frac{1}{2}\right)^x$

y = 1(2)^x

Multiple Choice

Write the equation of the exponential function for the given graph.

y = 1(2)^x

y = 2(1)^x

$y=2\left(\frac{1}{2}\right)^x$

$y=\frac{1}{2}\left(2\right)^x$

Writing Exponential Functions

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