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Section 6.1 : Exponential Functions

1. Given the function \(f\left( x \right) = {9^x}\) evaluate each of the following.
   1. \(f\left( { - 3} \right)\)
   2. \(f\left( { - 1} \right)\)
   3. \(f\left( 0 \right)\)
   4. \(\displaystyle f\left( {\frac{1}{2}} \right)\)
   5. \(\displaystyle f\left( {\frac{3}{2}} \right)\)
2. Given the function \(f\left( x \right) = {8^x}\) evaluate each of the following.
   1. \(\displaystyle f\left( { - \frac{2}{3}} \right)\)
   2. \(f\left( { - 1} \right)\)
   3. \(f\left( 0 \right)\)
   4. \(f\left( 2 \right)\)
   5. \(\displaystyle f\left( {\frac{5}{3}} \right)\)
3. Given the function \(f\left( x \right) = {\displaystyle \left( {\frac{1}{7}} \right)^x}\) evaluate each of the following.
   1. \(f\left( { - 2} \right)\)
   2. \(f\left( { - 1} \right)\)
   3. \(f\left( 0 \right)\)
   4. \(f\left( 2 \right)\)
   5. \(f\left( 4 \right)\)
4. Given the function \(f\left( x \right) = {\displaystyle \left( {\frac{1}{{16}}} \right)^x}\) evaluate each of the following.
   1. \(f\left( { - 2} \right)\)
   2. \(\displaystyle f\left( { - \frac{1}{4}} \right)\)
   3. \(f\left( 0 \right)\)
   4. \(f\left( 2 \right)\)
   5. \(\displaystyle f\left( {\frac{1}{4}} \right)\)
5. Sketch each of the following.
   1. \(f\left( x \right) = {\displaystyle \left( {\frac{1}{3}} \right)^x}\)
   2. \(g\left( x \right) = {\displaystyle \left( {\frac{1}{3}} \right)^x} + 2\)
   3. \(g\left( x \right) = {\displaystyle \left( {\frac{1}{3}} \right)^{x + 4}}\)
6. Sketch each of the following.
   1. \(f\left( x \right) = {5^x}\)
   2. \(g\left( x \right) = {5^x} - 4\)
   3. \(g\left( x \right) = {5^{x - 3}}\)
7. Sketch the graph of \(f\left( x \right) = {10^{x - 2}} + 6\) .
8. Sketch the graph of \(f\left( x \right) = {\displaystyle \left( {\frac{1}{7}} \right)^{x + 4}} - 1\) .
9. Sketch the graph of \(f\left( x \right) = {{\bf{e}}^{x + 1}} - 2\) .
10. Sketch the graph of \(f\left( x \right) = {{\bf{e}}^{x - 4}} - 1\) .