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

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

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Answer 1 · 2018-05-04T09:53:27

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Please read the explanation.

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 $color(red)x$ and the corresponding $color(red)(y$ values:

enter image source here

Construct both the graphs:

$color(green)"Graph 1:"$

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

enter image source here

Domain : $(-oo, oo)$

Range : $(0, oo)$

y-intercept : $(0,1)$

Horizontal Asymptote : $y=0$

$color(green)"Graph 2:"$

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

enter image source here

Domain : $(-oo, oo)$

Range : $(0, oo)$

y-intercept : $(0,1/0)$

Horizontal Asymptote : $y=0$

$color(green)"Graph 3:"$

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

Compare the behavior of both graphs:

enter image source here

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

Hope it helps.

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

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