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Homework: Graphing Inequalities and Absolute Values

Module by: Kenny M. Felder. E-mail the author

Summary: This module provides practice problems related to graphing inequalities and absolute values.

Exercise 1

The famous detectives Guy Noir and Nick Danger are having a contest to see who is better at catching bad guys. At 8:00 in the evening, they start prowling the streets of the city. They have twelve hours. Each of them gets 10 points for every mugger he catches, and 15 points for every underage drinker. At 8:00 the next morning, they meet in a seedy bar to compare notes. “I got 100 points,” brags Nick. If Guy gets enough muggers and drinkers, he will win the contest.

  • a. Label and clearly describe the relevant variables.
  • b. Write an inequality relating the variables you listed in part (a). I should be able to read it as “If this inequality is true, then Guy wins the contest.”
  • c. Graph the inequality from part (b).

Exercise 2

The graph below shows the function y=f(x)y=f(x) size 12{y=f \( x \) } {}.

Figure 1
A graph of the function f(x).
  • a. Graph y≤f(x)y≤f(x) size 12{y <= f \( x \) } {}. Your answer will either be a shaded region on a 2-dimensional graph, or on a number line.
  • b. Graph f(x)<0f(x)<0 size 12{f \( x \) <0} {}. Your answer will either be a shaded region on a 2-dimensional graph, or on a number line.

Exercise 3

x − 2y > 4 x − 2y > 4 size 12{x - 2y>4} {}

  • a. Graph.
  • b. Pick a point in your shaded region, and plug it back into our original equation x−2y>4x−2y>4 size 12{x - 2y>4} {}. Does the inequality work? (Show your work!)
  • c. Pick a point which is not in your shaded region, and plug it into our original equation x−2y>4x−2y>4 size 12{x - 2y>4} {}. Does the inequality work? (Show your work!)

Exercise 4

y > x 3 y > x 3 size 12{y>x rSup { size 8{3} } } {}

  • a. Graph. (Plot points to get the shape.)
  • b. Pick a point in your shaded region, and plug it back into our original equation y>x3y>x3 size 12{y>x rSup { size 8{3} } } {}. Does the inequality work? (Show your work!)
  • c. Pick a point which is not in your shaded region, and plug it into our original equation y>x3y>x3 size 12{y>x rSup { size 8{3} } } {}. Does the inequality work? (Show your work!)

Exercise 5

Graph: y+∣x∣<−∣x∣y+∣x∣<−∣x∣ size 12{y+ lline x rline < - lline x rline } {}. Think hard—you can do it!

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