AEF - Graph f(x) = a times b^x (Lesson)

Graph $f\left(x\right)=a\cdot b^x$ 

When a function is multiplied by a value, that value can affect the graph in a few different ways.  

 

The transformation affects the vertical component of the graph, so in order to graph one of these functions, we should graph the "base" function first, then apply the transformations.

Let's try graphing $y=2\cdot3^x$ .

First, graph y = 3^x by making a table.

x	y = 3x
-2	1/9
-1	1/3
0	1
1	3
2	9

 

 

Now since a = 2, that means the graph is vertically stretched by a factor of 2 so each y-value should be multiplied by 2.

x	$y=2\cdot3^x$
-2	2(1/9) = 2/9
-1	2(1/3) = 2/3
0	2(1) = 2
1	2(3) = 6
2	2(9) = 18

 

                                      

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

The graph of this function has an asymptote of y = 0.

Watch this video to try a few more:        

 

---

Transformations of Exponential Functions Practice

For 1-4, match each graph to its equation (5-8). 

For 5-8, explain the transformations of the equation. 

1.                       2. 

3.                        4. 

5. $y=-(\frac{1}{2})^x$

6. $f(x)=(\frac{1}{2})\cdot4^x$

7. $f(x)=2\cdot(\frac{1}{3})^x$

8. $y=-3^x$

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

IMAGES CREATED BY GAVS