Sketch the graph using transformations of a parent function (without a table of values). f(x) = | x | - 2
A) (Gridlines are spaced one unit apart.)
B) (Gridlines are spaced one unit apart.)
C) (Gridlines are spaced one unit apart.)
D) (Gridlines are spaced one unit apart.)

Question

Sketch the graph using transformations of a parent function (without a table of values). f(x) = | x | - 2
A) (Gridlines are spaced one unit apart.) 
B) (Gridlines are spaced one unit apart.) 
C) (Gridlines are spaced one unit apart.) 
D) (Gridlines are spaced one unit apart.)

Quizplus · Accepted Answer

The parent function for f(x) = | x | is a V-shaped graph passing through (0,0) with positive slope on both sides.

To graph f(x) = | x | - 2:
1. Start with the parent function f(x) = | x | and shift it down by 2 units (subtract 2 from every y-coordinate) to get f(x) = | x | - 2.
2. Since the parent function is symmetric about the y-axis, the resulting graph will also be symmetric about the y-axis.
3. The vertex (lowest point) of the graph will be at (0,-2) since we shifted the entire graph down by 2 units.

Therefore, the correct choice is C, which accurately represents all of these transformations.

Sketch the Graph Using Transformations of a Parent Function (Without