AnswersMathematics IIPractice ExamQuestion 33
33
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Practice Exam

Question 33 • Mathematics II

Which is the graph of g of x ? g of x is equal to 3 when x is less than 2; g of x is equal to negative x over 2 plus 2 when negative 2 is less than or equal to x and x is less than 2; g of x is equal to 2 x minus 3 when x is greater than or equal to 2

Answer
A
Image with description On a coordinate plane, a piecewise function has 3 connecting lines. The first line starts at (negative 5 comma 3) and goes horizontally to (negative 2 comma 3). The second line goes from (negative 2 comma 3) down to (2 comma negative 5). The third line starts at (2 comma negative 5) and goes up to (5 comma 1).
B
Image with description On a coordinate plane, a piecewise function has 3 lines. The first line starts at (negative 5 comma 3) and continues horizontally to (negative 2 comma 3). The second line has a closed circle at (negative 2 comma 2) and goes down to a closed circle at (2 comma 0). The third line has a closed circle at (2 comma 1) and goes up through (3 comma 3).
C
Image with description On a coordinate plane, a piecewise function has 3 lines. The first line starts at (negative 5 comma 3) and continues horizontally to (negative 2 comma 3). The second line has a closed circle at (negative 2 comma 2) and goes down to a closed circle at (2 comma 0). The third line has a closed circle at (2 comma negative 3) and goes up through (4 comma 1).
D
Image with description On a coordinate plane, a piecewise function has 3 connecting lines. The first line starts at (negative 5 comma 3) and goes horizontally to (negative 2 comma 3). The second line goes from (negative 2 comma 3) down to (2 comma 1). The third line starts at (2 comma 1) and goes up through (3 comma 3).

Explanation

The middle rule, g(x) = −x/2 + 2, gives g(−2) = 3 and approaches g(2) = 1, so its segment runs downward from (−2, 3) to (2, 1). The last rule gives g(2) = 1 and rises with slope 2, passing through (3, 3). Those points and directions match choice D. The first interval appears to be intended as x < −2; as written, x < 2 overlaps with the middle interval.

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