# How do you graph f(x)=3^(x - 2)?

May 4, 2018

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#### Explanation:

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Given the exponential function: color(red)(f(x)=3^(x-2)

Before graphing this function, create a data table:

The table should contain values for color(red)(x, corresponding values for color(red)(y=3^x) and color(red)(y=3^(x-2)

We include the base function: color(red)(y=3^x, since it provides an opportunity to examine the behavior of both the graphs by comparing them.

The table shows $\textcolor{red}{x}$ and the corresponding color(red)(y values:

Construct both the graphs:

$\textcolor{g r e e n}{\text{Graph 1:}}$

color(blue)("Graph of "y = f(x) = 3^x

Domain : $\left(- \infty , \infty\right)$

Range : $\left(0 , \infty\right)$

y-intercept : $\left(0 , 1\right)$

Horizontal Asymptote :$y = 0$

$\textcolor{g r e e n}{\text{Graph 2:}}$

color(blue)("Graph of "y = f(x) = 3^(x-2

Domain : $\left(- \infty , \infty\right)$

Range : $\left(0 , \infty\right)$

y-intercept : $\left(0 , \frac{1}{0}\right)$

Horizontal Asymptote :$y = 0$

$\textcolor{g r e e n}{\text{Graph 3:}}$

color(blue)("Graph of "y = f(x) = 3^(x) and y = f(x) = 3^(x-2)

Compare the behavior of both graphs:

Translation is horizontal for $y = f \left(x\right) = {3}^{x - 2}$ by color(red)(2 units.

Hope it helps.