Exercises - Exponential Functions and their Graphs

  1. Sketch the graph of $\displaystyle{y=3^x}$   $\ians{}$

  2. Sketch the graph of $\displaystyle{y = \left( \frac{1}{3} \right)^x = 3^{-x}}$   $\ians{}$

  3. Sketch the graphs of the following:

    1. $\displaystyle{y = 4^{x-2}}$   $\ians{}$

    2. $\displaystyle{y = 3^{-x}+1}$   $\ians{}$

    3. $\displaystyle{y = 4^{x^2}}$   $\ians{}$

    4. $\displaystyle{y = 4^{-x^2}}$   $\ians{}$

  4. Sketch the graphs of the following. Label intercepts and asymptotes, and give the domain and range.

    1. $\displaystyle{y = 2^x}$   $\ians{}$

    2. $\displaystyle{y = 2^{\,x^2}}$   $\ians{}$

    3. $\displaystyle{y = 2^{\,|x|}}$   $\ians{}$

    4. $\displaystyle{y = -2^{\,x}}$   $\ians{}$

    5. $\displaystyle{y = \left( \frac{3}{4} \right)^x}$   $\ians{}$

    6. $\displaystyle{y = 3^x - 3}$   $\ians{}$

    7. $\displaystyle{y = 3^{\,-x\,+1\,}}$   $\ians{}$