the graph shows that $f(x)=3^{x}$ is translated horizontally and vertically to create the function…

the graph shows that $f(x)=3^{x}$ is translated horizontally and vertically to create the function $g(x)=3^{x - h}+k$. what is the value of $h$? -2 -1 1 2

the graph shows that $f(x)=3^{x}$ is translated horizontally and vertically to create the function $g(x)=3^{x - h}+k$. what is the value of $h$? -2 -1 1 2

Answer

Explanation:

Step1: Recall horizontal - translation rule

For an exponential function (y = a^{x - h}+k), a positive (h) value shifts the graph of (y = a^{x}) to the right by (h) units and a negative (h) value shifts it to the left by (|h|) units.

Step2: Analyze the graph

The graph of (f(x)=3^{x}) passes through the point ((0, 1)) (since (3^{0}=1)). The graph of (g(x)=3^{x - h}+k) passes through the point ((2,1)).

Step3: Determine the value of (h)

We know that for the horizontal - shift of the point ((0,1)) on (y = 3^{x}) to the point ((2,1)) on (y = 3^{x - h}+k), we use the formula (x'=x - h). Here, (x = 0), (x'=2). Substituting into (x'=x - h), we get (2=0 - h), so (h=- 2).

Answer:

-2