Questions on Power Functions

What's On This Page

This page contains sample problems on power functions. They are for Self-assessment and Review.

Each problem (or group of problems) has an "answer button" ANSWER which you can click to look at an answer. Some solutions have a "further explanation button" Explain which you can click to see a more complete, detailed solution.

What to Do

To gain the most benefit from these problems,

Work the problems on your own. Write down your solutions BEFORE looking at any answers.

Use a graphing calculator as appropriate. A graphing calculator can be used to verify that your answers "make sense" or "look right".

If you have difficulties with this material, please contact your instructor. (See Getting Help in Stage 1.) Power functions should be familiar to you and require at most a quick review.

1. Evaluate the following expressions:

  1. 81/3, 8-1/3

  2. 82/3, 8-2/3

  3. 45/2, 274/3, 16-3/2

ANSWER

2.In the table below you can see the values of three different functions. Two are power functions: one has the form f(t) = at2, while the other has the form f(t) = bt3. The third is an exponential function of the form f(t) = kbt. Which is which and how can you tell?

tF1(t)tF2(t)tF3(t)
1.02.502.22.04.8
1.24.321.02.642.25.81
1.46.862.03.172.46.91
1.610.243.03.802.68.11
1.814.584.04.562.89.41
2.020.05.05.473.010.8

ANSWER

3. For each of the following, either solve for x or explain why no solution exists. Symbolic answers such as x = 4(1/3) are sought rather than decimal answers such as 1.5874.

  1. 3 x2.2 = 6.

  2. 3 x2.2 = -6.

  3. x -4 = 1.7

  4. x -4 = -1.7
ANSWER

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