Powers and Exponential Functions: Practice Exercises

Here are various Exercises to accompany the section Powers and Exponential Functions.  

Graphing Exponential Functions

1. Use our transformational graphing technique to graph the following exponential functions:
   1. f(x) = 3^-x - 2
   2. g(x) = -3·2^{x + 1} + 1
   3. h(x) = 4·5^{x - 2} - 3
   4. k(x) = -3^{1 - x} + 2

   Solution.

2. Fill-in-the-blanks to create a formula for an exponential function, then use our transformational graphing technique to graph it.

   y = __·__^{(__x + __)} + __

   Note: The expression in the parentheses is the exponent of the expression.

   Repeat this Exercise as often as necessary until you are confident in your ability to plot exponential graphs.

   Solution.

Symmetries of Exponential Functions

1. Use our transformational graphing technique to graph the following exponential functions:
   1. f(x) = 2^{-2x + 3}
   2. g(x) = -3·9^{(x + 1)/2} + 1
   3. h(x) = -2·(1/3)^{-x - 2} + 1
   4. k(x) = 8·(1/4)^x

   Solution.

2. In the previous Exercise, there are only two different functions, because there are two pairs of equal expressions.  Using the rules of exponents, determine which two functions are equal.  Do their graphs look the same?  Why or why not?

   Solution.

Go to Applications of Exponential Functions .

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