2.7 Graphing inequalities and absolute values

• A

  Put into a sort of $y=\text{mx}+b$ format, except that it will be an inequality.

• B

  Now, ignore the fact that it is an inequality—pretend it is a line, and graph that line.

• C

  Now, to graph the inequality, shade in the area either above the line, or below the line, as appropriate.
  Does $y$ have to be less than the values on the line, or greater than them?

• D

  Test your answer. Choose a point (any point) in the region you shaded, and test it in the inequality. Does the inequality work? (Show your work.)

• E

  Choose a point (any point) in the region you did not shade, and test it in the inequality. Does the inequality work? (Show your work.)

• A

  Graph the inequality, using the same steps as above.

• B

  Test your answer by choosing one point in the shaded region, and one point that is not in the shaded region. Do they give you the answers they should? (Show your work.)

$y=\mid x\mid$

• A

  Create a table of points. Your table should include at least two positive $x$ -values, two negative $x$ -values, and $x=0$ .

• B

  Graph those points, and then draw the function.

$y=\mid x\mid +3$ . Graph this without a table of points, by remembering what“adding 3”does to any graph. (In other words, what will these $y$ -values be like compared to your $y$ -values in #3?)

$y=-\mid x\mid$ . Graph this without a table of points, by remembering what“multiplying by–1”does to any graph. (In other words, what will these $y$ -values be like compared to your $y$ -values in #3?)

Now, let’s put it all together!!!

• A

  Graph $y=-\mid x\mid +2$ .

• B

  Graph $y\ge \mid x\mid +2$ . Your answer will either be a shaded region on a 2-dimensional graph, or on a number line.

• C

  Test your answer by choosing one point in the shaded region, and one point that is not in the shaded region. Do they give you the answers they should? (Show your work.)

• D

  Graph–|x|+2<0. Your answer will either be a shaded region on a 2-dimensional graph, or on a number line.

• E

  Test your answer by choosing one point in the shaded region, and one point that is not in the shaded region. Do they give you the answers they should? (Show your work.)

Extra for experts:

• A

  Graph it. Think hard about what that +4 and that 3 will do. Generate a few points if it will help you!

• B

  Test your answer by choosing one point in the shaded region, and one point that is not in the shaded region. Do they give you the answers they should? (Show your work.)