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Lesson Menu Five-Minute Check (over Lesson 2–7) CCSS Then/Now New Vocabulary Example 1:Dashed Boundary Example 2:Real-World Example: Solid Boundary Example 3:Absolute Value Inequality

Over Lesson 2–7 5-Minute Check 1 Identify the type of function represented by the graph. Graph f(x) = |x + 2|. Identify the domain and range.

Over Lesson 2–7 5-Minute Check 1 A.piecewise-defined B.absolute value C.quadratic D.linear Identify the type of function represented by the graph.

Over Lesson 2–7 5-Minute Check 2 A.piecewise-defined B.absolute value C.quadratic D.linear Identify the type of function represented by the graph.

Over Lesson 2–7 5-Minute Check 3 A.D = all reals R = all reals B.D = all reals R = all nonnegative reals C.D = all reals less than –2 R = all reals D.D = all reals R = all reals less than –1 Graph f(x) = |x + 2|. Identify the domain and range.

CCSS Content Standards A.CED.3 Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. Mathematical Practices 1 Make sense of problems and persevere in solving them.

Then/Now You described transformations on functions. Graph linear inequalities. Graph absolute value inequalities.

Vocabulary linear inequality boundary

Example 1 Dashed Boundary Graph x – 2y < 4. The boundary is the graph of x – 2y = 4. Since the inequality symbol is <, the boundary will be dashed.

Example 1 Graph x – 2y < 4. Test (0, 0). Original inequality (x, y) = (0, 0) Shade the region that contains (0, 0). Answer: Dashed Boundary True

Example 1 Which graph is the graph of 2x + 5y > 10? A.B. C.D.

Example 2 Solid Boundary A. EDUCATION One tutoring company advertises that it specializes in helping students who have a combined score on the SAT that is 900 or less. Write an inequality to describe the combined scores of students who are prospective tutoring clients. Let x represent the verbal score and y the math score. Graph the inequality. Let x be the verbal part of the SAT and let y be the math part. Since the scores must be 900 or less, use the  symbol.

Example 2 Solid Boundary Answer: x + y ≤ 900 Verbalmath part partand together are at most900. xy  900+

Example 2 Solid Boundary B. Does a student with verbal score of 480 and a math score of 410 fit the tutoring company’s guidelines? The point (480, 410) is in the shaded region, so it satisfies the inequality. Answer: Yes, this student fits the tutoring company’s guidelines.

Example 2 A.s + c ≥ 60 B.s + c ≤ 60 C.s + c < 60 D.s + c > 60 A. CLASS TRIP Two social studies classes are going on a field trip. The teachers have asked for parent volunteers to also go on the trip as chaperones. However, there is only enough seating for 60 people on the bus. What is an inequality to describe the number of students and chaperones that can ride on the bus?

Example 2 B. Can 15 chaperones and 47 students ride on the bus? A.Yes; the point (15, 47) lies in the shaded region. B.No; the point (15, 47) lies outside the shaded region.

Example 3 Absolute Value Inequality (x, y) = (0, 0) Original inequality True Shade the region that contains (0, 0). Since the inequality symbol is ≥, the graph of the related equation y = |x| – 2 is solid. Graph the equation. Test (0, 0).

Example 3 A.B. C.D.

End of the Lesson