Transformations Involving Exponential Functions Use the graph of f(x) = 3^x to obtain the graph of g(x) = 3^x+ 1.

Question

Transformations Involving Exponential Functions

Use the graph of [latex]f(x)=3^x[/latex] to obtain the graph of [latex]g(x)=3^{x+1}[/latex].

Accepted Answer

The graph of [latex]g(x)=3^{x+1}[/latex] is the graph of [latex]f(x)=3^x[/latex] shifted 1 unit to the left.

	Begin with a table showing some of the coordinates for f.
x	[latex]f(x)=3^x[/latex]
-2	[latex]f(-2)=3^{-2}=\frac{1}{9}[/latex]
-1	[latex]f(-1)=3^{-1}=\frac{1}{3}[/latex]
0	[latex]f(0)=3^0=1[/latex]
1	[latex]f(1)=3^1=3[/latex]
2	[latex]f(2)=3^2=9[/latex]

	Begin with a table showing some of the coordinates for f.
x	$f(x)=3^x$
-2	$f(-2)=3^{-2}=\frac{1}{9}$
-1	$f(-1)=3^{-1}=\frac{1}{3}$
0	$f(0)=3^0=1$
1	$f(1)=3^1=3$
2	$f(2)=3^2=9$

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