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PEGEF - Shift Exponential Functions (Lesson)

Shift Exponential Functions

Now that we have stretched, compressed, and reflected the exponential functions, we should practice shifting them. The shifts for exponential functions are described below:

f of x equals a times b to the x minus h plus k

Here is an example:

$LaTeX: y=2\cdot3^{x-4}+1$ $y=2\cdot3^{x-4}+1$

a = 2

b = 3

h = 4

k = 1

From our previous lesson, we know this stretches the graph vertically by a factor of 2

The base is greater than 1, so this function will be exponential growth

The value of h is 4, so the graph shifts right 4.

The value of k is 1, so the graph shifts up 1

Let's try graphing $LaTeX: y=2\cdot3^{x-4}+1$ $y=2\cdot3^{x-4}+1$

1. We will start by graphing the base function y = 3^x.

graph of y equals three to the x

2. Now we will stretch vertically by a factor of 2.

stretch vertically by a factor of 2

3. Now we will shift right 4 and up 1.

shift right 4 and up 1

Notice that the asymptote of y = 0 has been shifted with the function up 1. So the new asymptote is y =1.

Graph of an asymptote

Watch this video to try a few more.

More Transformations of Exponential Functions Practice

Match the items.

$LaTeX: f\left(x\right)=-2\cdot3^{x+2}-1$ $f\left(x\right)=-2\cdot3^{x+2}-1$
$LaTeX: y=\frac{1}{2}\cdot3^{x+2}-1$ $y=\frac{1}{2}\cdot3^{x+2}-1$
$LaTeX: f\left(x\right)=2\cdot3^{x-2}+1$ $f\left(x\right)=2\cdot3^{x-2}+1$
$LaTeX: y=-3^{x-1}+2$ $y=-3^{x-1}+2$

TO VIEW THE SOLUTIONS ONCE YOU HAVE PRACTICED, CLICK HERE. Links to an external site.

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