AEF - 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:

 
 

Here is an example:

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

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

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

Step 3: Now we will 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.

Watch this video to try a few more.

     

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More Transformations of Exponential Functions Practice

Name the transformations for each function.

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

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