Powers and Proportions: Practice Exercises

Here are various Exercises to accompany the section Powers and Proportions.  

Power Functions

  1. Use the general properties of power functions to match the formulas with their graphs below:
    1. x5
    2. x4
    1. x3
    2. x2
    1. 1/x3
    2. 1/x
    1. 1/x4
    2. 1/x6

    Solution.

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

    Solution.

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

    y = __(__x + __)__ + __

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

    Solution.

Proportions

  1. Translate the following verbal descriptions, using the terminology of proportions, into functional equations relating the indicated variables.
    1. The surface area, A, of a cube is directly proportional to the square of the length, x, of one side.
    2. The resistance, R, of a piece of wire is directly proportional to its length, L, and inversely proportional to the square of its diameter, d.

    Solution.

  2. Translate the following functional equations relating the given variables into verbal descriptions, using the terminology of proportions. 
    1. V = kr3
    2. y = k/x4
    3. h = kV/r2

    Solution.

  3. Follow the given instructions to investigate the given applied situation. 
    1. The speed, s (in mph.), you travel in your car (in fourth gear) is directly proportional to speed of your engine, r (in thousands of rpm.), indicated on your tachometer.  Give an expression for s as a function r, with a constant of proportionality, k.
    2. At one point, you notice that at 50 mph., your tachometer reads 30,000 rpm.  Use this information to solve for k.
    3. If your tachometer reads 24,000 rpm., use your equation to predict your speed, s.

    Solution.

Go to Polynomials and Roots .

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