Practice Test

Question 14 • Mathematics III

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 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 Cartesian coordinate system, the x-axis labeled from negative 8 to 2 in increments of 1 and y-axis labeled from negative 3 to 7 in increments of 1. A v shaped curve is plotted. The curve's vertex is at (negative 4 comma negative 1). From this point, the curve opens upwards, with its left branch passing through (negative 5 comma 2) and (negative 6 comma 5), and its right branch passing through (negative 3 comma 2) and (negative 2 comma 5).

Image with description On a Cartesian coordinate system, the x-axis labeled from negative 9 to 1 in increments of 1 and y-axis labeled from negative 7 to 3 in increments of 1. A v shaped curve is plotted. The curve's vertex is at (negative 4 comma 1). From this point, the curve opens downwards, with its left branch passing through (negative 5 comma negative 2) and (negative 6 comma negative 5), and its right branch passing through (negative 3 comma negative 2) and (negative 2 comma negative 5).

Image with description On a Cartesian coordinate system, the x-axis labeled from negative 3 to 7 in increments of 1 and y-axis labeled from negative 7 to 3 in increments of 1. A v shaped curve is plotted. The curve's vertex is at (4 comma negative 1). From this point, the curve opens downwards, with its left branch passing through (3 comma negative 4) and (2 comma negative 7), and its right branch passing through (5 comma negative 4) and (6 comma negative 7).

Explanation

The function f(x) = 3|x − 4| + 1 is in the form a|x − h| + k, so its vertex is (h, k) = (4, 1). Since the coefficient 3 is positive, the V opens upward. One unit from the vertex, at x = 3 or x = 5, the function’s value is 3(1) + 1 = 4, matching choice A’s graph.

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