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Section 6.1 : Exponential Functions

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