Graphing and Linear Functions: Practice Exercises

Here are various Exercises to accompany the section Graphing and Linear Functions.  Some Exercises are designed to be done with a partner and to be graded by the partner.

Arithmetic Operations and Lines

  1. Fill in the following chart and sketch the corresponding linear function, f(x) = -3x - 2:
    Corresponding
    Algebraic formula    		 x x 3x -3x -3x - 2
    Geometric Effect   Take the graph of the
    identity function    		      
    Numerical Effect Take the input Apply the
    identity function    		      
    Numerical 
    Results    		 Inputs Outputs
    -1        
    0        
    1        

    Solution.

  2. Make up your own linear function, by filling in the blanks, g(x) = __x + __.  Note: You can use positive or negative numbers, including fractions, in each slot.  Fill in the following chart and sketch a graph for your function.
    Corresponding
    Algebraic formula    		 x x      
    Geometric Effect   Take the graph of
    the identity function    		      
    Numerical Effect Take the input Apply the
    identity function    		      
    Numerical 
    Results    		 Inputs Outputs
    -1        
    0        
    1        

    Solution.

  3. Match each equation with the corresponding graph.  Hint: Use the geometric description of linear equations given in the text.
    1. y = -2x - 1
    2. y = 1
    3. y = 2x - 1
    4. y = -x - 2
    5. x = 1
    6. y = x - 1

     

    Solution.

The Equation of a Linear Function

  1. Using the description of linear equations in the text, give a formula for each of the following linear functions:
    1. x y = f(x)
      -1
      0
      1       		-4
      -1
      2
    2. x y = g(x)
      0
      1
      2       		6
      5.5
      5
    3.  
    4.  
    5. b = p(m), where b is the balance (in dollars) after m months on an (interest-free) car loan of $5000 that your parents made you, assuming that you pay them back $200 per month.  Hint: Make a table of values.
    6. F = q(C), where C is the temperature in degrees Celsius and  F is the temperature in degrees Fahrenheit.  Hint: When C = 0, F = 32 (i.e., the freezing point of water), and when the temperature goes up 1 degree Celsius, it goes up 1.8 degrees Fahrenheit. 

    Solution.

  2. Work with your partner to create more practice Exercises.

    1. Have your partner choose his/her own linear function (cf. a previous Exercise), and keep it hidden from you.  Then have your partner make a table of values at x = -1, 0, 1, 2 for his/her function, and show it to you.  Try to guess your partner's function.
    2. Have your partner choose his/her own linear function (cf. a previous Exercise), and keep it hidden from you.  Then have your partner make define a new function with this formula in XFunctions:

      Try to guess your partner's function by looking only at its graph.

    3. Have your partner imagine an applied situation similar to the ones given in the text, where one quantity begins at a given amount and changes as a multiple of some other quantity.  Have him/her describe this situation to you, and see if you can write down a correct equation.

    Solution.

Modeling Linear Functions

  1. Using the concept of slope in the text, determine which of the following represent linear functions, and give a formula for those that are linear:
    1. x y = f(x)
      5
      10
      15       		7
      2
      -3
    2. x y = g(x)
      2
      6
      8       		4
      2
      0
    3. x y = h(x)
      1
      -1
      5       		10
      6
      18
    4.  
    5.  
    6.  

    Solution.

  2. Work with your partner to create more practice Exercises.
    1. Have your partner choose his/her own linear function (cf. a previous Exercise), and keep it hidden from you.  Then have your partner make a table of values at four different inputs for his/her function, and show it to you.  Try to guess your partner's function.
    2. Have your partner choose his/her own linear function (cf. a previous Exercise), and keep it hidden from you.  Then have your partner make define a new function with this formula in XFunctions:

      Try to guess your partner's function by looking only at its graph.

    Solution.

Go to Pre-Composition and Graphing .

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