Algebra - Exponential Functions

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Section 6.1 : Exponential Functions

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1. Given the function \(f\left( x \right) = {4^x}\) evaluate each of the following.

\(f\left( { - 2} \right)\)
\(f\left( {\displaystyle - \frac{1}{2}} \right)\)
\(f\left( 0 \right)\)
\(f\left( 1 \right)\)
\(f\left( {\displaystyle \frac{3}{2}} \right)\)

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a \(f\left( { - 2} \right)\) Show Solution

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

\[f\left( { - 2} \right) = {4^{ - 2}} = \frac{1}{{{4^2}}} = \require{bbox} \bbox[2pt,border:1px solid black]{{\frac{1}{{16}}}}\]

b \(f\left( {\displaystyle - \frac{1}{2}} \right)\) Show Solution

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

\[f\left( { - \frac{1}{2}} \right) = {4^{ - \,\,\frac{1}{2}}} = \frac{1}{{{4^{\frac{1}{2}}}}} = \frac{1}{{\sqrt 4 }} = \require{bbox} \bbox[2pt,border:1px solid black]{{\frac{1}{2}}}\]

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.

\[f\left( 0 \right) = {4^0} = \require{bbox} \bbox[2pt,border:1px solid black]{1}\]

d \(f\left( 1 \right)\) Show Solution

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

\[f\left( 1 \right) = {4^1} = \require{bbox} \bbox[2pt,border:1px solid black]{4}\]

e \(f\left( {\displaystyle \frac{3}{2}} \right)\) Show Solution

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

\[f\left( {\frac{3}{2}} \right) = {4^{\,\frac{3}{2}}} = {\left( {{4^{\frac{1}{2}}}} \right)^3} = {2^3} = \require{bbox} \bbox[2pt,border:1px solid black]{8}\]