AnswersAlgebra 2 with ProbabilityMathematical Modeling — TestQuestion 18
18
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Mathematical Modeling — Test

Question 18 • Algebra 2 with Probability

A function, h of x , is defined as shown. h of x is equal to 1 fourth x minus 4 when x is less than or equal to 0; h of x is equal to 1 third x minus when 0 is less than x and x is less than or equal to 3; h of x is equal to 1 half x minus 2 when x is greater than or equal to 4 Which graph represents h of x ?

Answer
A
Image with description A coordinate plane showing a piecewise function labeled h of x across all 4 quadrants. The horizontal x axis is labeled from negative 4 to 6, and the vertical y axis is labeled from negative 5 to 5. The function consists of three distinct line segments. The first segment starts at the second quadrant at negative 4 comma 3 and extends upward to the right, ending at the y axis with a solid circle at 0 comma 4. The second segment begins directly below at 0 comma 3 with an open circle and extends upward to the right, ending with a solid circle at 3 comma 4. The third segment starts at 4 comma 4 with a solid circle and extends upward to the right, ending in the first quadrant at 6 comma 5.
B
Image with description A coordinate plane showing a piecewise function labeled h of x across all 4 quadrants. The horizontal x axis is labeled from negative 4 to 6, and the vertical y axis is labeled from negative 5 to 5. The function consists of three distinct line segments. The first segment starts on the x axis at negative 4 comma 0 and extends upward to the right, ending at the y axis with a solid circle at 0 comma 1. The second segment begins directly below at 0 comma negative 3 with an open circle and extends upward to the right, ending with a solid circle at 3 comma negative 2. The third segment starts at 4 comma negative 2 with a solid circle and extends upward to the right, ending at 6 comma negative 1.
C
Image with description A coordinate plane showing a piecewise function labeled h of x across all 4 quadrants. The horizontal x axis is labeled from negative 4 to 6, and the vertical y axis is labeled from negative 5 to 5. The function consists of three distinct line segments. The first segment starts at the fourth quadrant near negative 4 comma negative 5 and extends upward to the right, ending at the y axis with a solid circle at 0 comma negative 4. The second segment begins directly above at 0 comma negative 3 with an open circle and extends upward to the right, ending with a solid circle at 3 comma negative 2. The third segment starts at 4 comma 0 with a solid circle and extends upward to the right, ending at 6 comma 1.
D
Image with description A coordinate plane showing a piecewise function labeled h of x across all 4 quadrants. The horizontal x axis is labeled from negative 4 to 6, and the vertical y axis is labeled from negative 5 to 5. The function consists of three distinct line segments. The first segment starts on the x axis at negative 4 comma 0 and extends upward to the right, ending at the y axis with a solid circle at 0 comma 1. The second segment begins directly below at 0 comma negative 1 with an open circle and extends upward to the right, ending with a solid circle at 3 comma 0. The third segment starts at 4 comma negative 2 with a solid circle and extends upward to the right, ending at 6 comma negative 1.

Explanation

For the first piece, h(0) = −4, and h(−4) = −5, so its line ends at the solid point (0, −4) and extends through (−4, −5). The middle piece starts with an open point at (0, −3) and reaches (3, −2). The last piece begins at x = 4 with h(4) = 0, so it has a solid point at (4, 0) and rises to (6, 1). These points and endpoint types match graph C.

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