Question

graph the given functions, f and g, in the same rectangular coordinate system. describe how the graph of g is related to the graph of f.

\\(f(x) = |x|\\)
\\(g(x) = |x| - 5\\)

use the graphing tool to graph the functions.

how is the graph of g related to the graph of f?

a. the graph of g is the graph of f shifted 5 units vertically down.
b. the graph of g is the graph of f shifted 5 units vertically up.
c. the graph of g is the graph of f shifted 5 units horizontally left.
d. the graph of g is the graph of f shifted 5 units horizontally right.

Explanation:

Identify the parent function

Using the Absolute Value Functions knowledge point

$$ f(x) = |x| $$

Analyze the transformation

Using the Absolute Value Functions knowledge point

$$ g(x) = f(x) - 5 = |x| - 5 $$

Determine the geometric effect

Using the Absolute Value Functions knowledge point
Subtracting \(5\) from the output shifts the graph vertically downward by \(5\) units.

Answer:

• (A) The graph of g is the graph of f shifted 5 units vertically down (Correct answer)
• (B) The graph of g is the graph of f shifted 5 units vertically up
• (C) The graph of g is the graph of f shifted 5 units horizontally left
• (D) The graph of g is the graph of f shifted 5 units horizontally right