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### Section 6-1 : Exponential Functions

2. Given the function $$f\left( x \right) = {\left( {\displaystyle \frac{1}{5}} \right)^x}$$ evaluate each of the following.

1. $$f\left( { - 3} \right)$$
2. $$f\left( { - 1} \right)$$
3. $$f\left( 0 \right)$$
4. $$f\left( 2 \right)$$
5. $$f\left( 3 \right)$$

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a $$f\left( { - 3} \right)$$ Show Solution

All we need to do here is plug in the $$x$$ and do any quick arithmetic we need to do.

$f\left( { - 3} \right) = {\left( {\frac{1}{5}} \right)^{ - 3}} = {\left( {\frac{5}{1}} \right)^3} = \frac{{{5^3}}}{{{1^3}}} = \require{bbox} \bbox[2pt,border:1px solid black]{{125}}$

b $$f\left( { - 1} \right)$$ Show Solution

All we need to do here is plug in the $$x$$ and do any quick arithmetic we need to do.

$f\left( - \right) = {\left( {\frac{1}{5}} \right)^{ - \,1}} = {\left( {\frac{5}{1}} \right)^1} = \require{bbox} \bbox[2pt,border:1px solid black]{5}$

c $$f\left( 0 \right)$$ Show Solution

All we need to do here is plug in the $$x$$ and do any quick arithmetic we need to do.

$f\left( 0 \right) = {\left( {\frac{1}{5}} \right)^0} = \require{bbox} \bbox[2pt,border:1px solid black]{1}$

d $$f\left( 2 \right)$$ Show Solution

All we need to do here is plug in the $$x$$ and do any quick arithmetic we need to do.

$f\left( 2 \right) = {\left( {\frac{1}{5}} \right)^2} = \frac{{{1^2}}}{{{5^2}}} = \require{bbox} \bbox[2pt,border:1px solid black]{{\frac{1}{{25}}}}$

e $$f\left( 3 \right)$$ Show Solution

All we need to do here is plug in the $$x$$ and do any quick arithmetic we need to do.

$f\left( 3 \right) = {\left( {\frac{1}{5}} \right)^3} = \frac{{{1^3}}}{{{5^3}}} = \require{bbox} \bbox[2pt,border:1px solid black]{{\frac{1}{{125}}}}$