Square Root and Absolute Value Functions — Test

Question 14 • Algebraic Reasoning

Which graph represents the function f of x is equal to absolute value of x minus 4 ?

Answer

Image with description A coordinate plane with a V-shaped graph opening upward. The x-axis and y-axis are labeled from negative 6 to 6 in increments of 1. The graph has its vertex at 4 comma 0, ascends to the left passing through 0 comma 4, and ascends to the right passing through 5 comma 1.

Image with description A coordinate plane with a V-shaped graph opening upward. The x-axis and y-axis are labeled from negative 6 to 6 in increments of 1. The graph has its vertex at 0 comma negative 4, ascends to the left passing through negative 5 comma 1, and ascends to the right passing through 4 comma 0.

Image with description A coordinate plane with a V-shaped curve opening upward with its vertex at 0 comma negative 4. The curve passes through the point negative 4 comma 0 and the point 4 comma 0, with the left side rising at a slope of negative 1 and the right side rising at a slope of 1.

Image with description A coordinate plane with a V-shaped graph opening upward. The x-axis and y-axis are labeled from negative 6 to 6 in increments of 1. The graph has its vertex at negative 4 comma 0, ascends to the left passing through negative 6 comma 2, and ascends to the right passing through 0 comma 4.

Explanation

For f(x) = |x − 4|, the graph of |x| is shifted 4 units to the right. Its vertex is therefore at (4, 0), and it passes through (0, 4). Choice A shows this graph. Choice C instead has its vertex at (0, −4), which would represent |x| − 4.

AI-written and checked against the verified answer.

More from this Course

Test

Test

Test