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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. $$f\left( - \frac{1}{2}} \right$$
3. $$f\left( 0 \right)$$
4. $$f\left( 1 \right)$$
5. $$f\left( \frac{3}{2}} \right$$
Solution
2. Given the function $$f\left( x \right) = {\left( \frac{1}{5}} \right)^x$$ 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