Math Problem Statement

Find the domain, range, and vertex for each absolute value function provided on the worksheet.

Solution

The image you uploaded contains a worksheet on graphing absolute value equations, which asks to find the domain, range, and vertex for each function. Here's how to approach each problem:

General form of an absolute value function:

y=axh+ky = a |x - h| + k

  • Vertex: (h,k)(h, k)
  • Domain: Always (,)(-\infty, \infty) since absolute value functions are defined for all xx.
  • Range: Depends on aa (if a>0a > 0, the function opens upward; if a<0a < 0, it opens downward).

Now, let’s solve the first few problems:

9. y=2xy = 2 |x|

  • Vertex: Since there is no shift in xx or yy, the vertex is at (0,0)(0, 0).
  • Domain: ( (-\infty,

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Math Problem Analysis

Mathematical Concepts

Absolute Value Functions
Graphing
Algebra

Formulas

General Form of Absolute Value Function: y = a |x - h| + k

Theorems

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Suitable Grade Level

Grades 9-12