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

Graph $LaTeX: f\left(x\right)=a\cdot b^x$ $f\left(x\right)=a\cdot b^x$

Recall from our lesson on transformations of functions that when a function is multiplied by a value, that value can do a few things.

f of x equals a times b to the x explanation

The transformation effects 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 $LaTeX: y=2\cdot3^x$ $y=2\cdot3^x$ .

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

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

Exponential Graph

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

Exponential Graph

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

Watch this video to try a few more:

Transformations of Exponential Functions Practice

Match each equation to its graph and each equation to the appropriate transformations:

5. y = -(1/2)^x

6. f(x) = (1/2)4^x

7. f(x) = 2(1/3)^x

8. y = -3^x

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

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

Graph f(x)=a⋅bxf\left(x\right)=a\cdot b^x

Transformations of Exponential Functions Practice

Graph $LaTeX: f\left(x\right)=a\cdot b^x$ $f\left(x\right)=a\cdot b^x$