Practice Test

Question 5 • Precalculus

Which of the following is the graph of f of x is equal to 3 start absolute value x minus 4 end absolute value plus 1 ?

Answer

Image with description On a coordinate plane, the scale on the x axis ranges from negative 9 to 1 in increments of 1, and the scale on the y axis ranges from negative 7 to 3 in increments of 1. The V-shaped graph opening downward has a vertex at (negative 4 comma 1) and the graph passes through the points (negative 6 comma negative 5) and (negative 2 comma negative 5).

Image with description On a coordinate plane, the scale on the x axis ranges from negative 8 to 2 in increments of 1, and the scale on the y axis ranges from negative 3 to 7 in increments of 1. The V-shaped graph opening upward has a vertex at (negative 4 comma negative 1) and the graph passes through the points (negative 6 comma 5) and (negative 2 comma 4).

Image with description On a coordinate plane, the scale on the x axis ranges from negative 1 to 9 in increments of 1, and the scale on the y axis ranges from negative 3 to 7 in increments of 1. The V-shaped graph opening upward has a vertex at (4 comma 1) and the graph passes through the points (3 comma 4) and (5 comma 4).

Image with description On a coordinate plane, the scale on the x axis ranges from negative 3 to 7 in increments of 1, and the scale on the y axis ranges from negative 7 to 3 in increments of 1. The V-shaped graph opening downward has a vertex at (4 comma negative 1) and the graph passes through the points (3 comma negative 4) and (5 comma negative 4).

Explanation

For f(x) = 3|x − 4| + 1, the absolute value graph has its vertex at (4, 1), since x − 4 is zero when x = 4. The positive coefficient 3 means the V opens upward. One unit to either side of x = 4, the output is 3(1) + 1 = 4, so the graph passes through (3, 4) and (5, 4). Choice D matches these features.

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