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Practice Test Answers

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1
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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

A
Image with description A coordinate plane displays the x-axis labeled from negative 5 to 5 in increments of 1 and the y-axis labeled from negative 5 to 5 in increments of 1. A piecewise graph labeled g of x consists of three parts. A horizontal ray at y equals 3 extends leftward and ends with a closed circle at negative 2 comma 2. A decreasing line segment connects the closed point negative 2 comma 2 to an open circle at 2 comma 0. A third line segment begins with a closed circle at 2 comma 1 and rises to approximately 4 comma 5.
B
Image with description A coordinate plane displays the x-axis labeled from negative 5 to 5 in increments of 1 and the y-axis labeled from negative 5 to 5 in increments of 1. A piecewise graph labeled g of x consists of three parts. A horizontal line at y equals 3 extends from approximately x equals negative 5 to an open circle at negative 2 comma 3. A decreasing line segment begins with a closed circle at negative 2 comma 2 and ends with an open circle at 2 comma 0. An increasing line segment begins with a closed circle at 2 comma negative 3 and rises to approximately the point 5 comma 3.
C
Image with description A coordinate plane displays the x-axis labeled from negative 5 to 5 in increments of 1 and the y-axis labeled from negative 5 to 5 in increments of 1. A piecewise graph labeled g of x consists of three connected parts. A horizontal line at y equals 3 extends from approximately x equals negative 5 to x equals negative 2. A decreasing line segment connects the point negative 2 comma 3 to the point 2 comma 1. An increasing line segment then connects the point 2 comma 1 to approximately the point 4 comma 5.
D
Image with description A coordinate plane displays the x-axis labeled from negative 5 to 5 in increments of 1 and the y-axis labeled from negative 5 to 5 in increments of 1. A piecewise graph labeled g of x consists of three parts. A horizontal line at y equals 3 extends from approximately x equals negative 5 to x equals negative 2. A decreasing line segment connects the point negative 2 comma 3 to the point 2 comma negative 5. An increasing line segment then connects the point 2 comma negative 5 to approximately the point 5 comma 1.
2
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Which statement best compares the graphs of f of x is equal to lfloor x rfloor and f of x is equal to lceil x rceil ?

A
The two graphs are exactly the same.
B
The graph of f of x is equal to lceil x rceil is shifted up compared to the graph of f of x is equal to lfloor x rfloor , and the open and closed circles are the same.
C
The open and closed circles are reversed.
D
The graph of f of x is equal to lceil x rceil is shifted up compared to the graph of f of x is equal to lfloor x rfloor , and the open and closed circles are reversed.
3

Which is the graph of the piecewise-function f of x ? f of x is equal to negative x plus 1 when x is less than or equal to 0; f of x is equal to x plus 1 when x is greater than 0

A
Image with description A coordinate plane with a horizontal axis labeled x and a vertical axis labeled f (x). The scale on both axes ranges from negative 5 to 5 with an interval of 1 unit. An inverted, downward-opening V-shaped line has its vertex at 1 comma 0. To the left of the vertex, the line passes through 0 comma negative 1, negative 1 comma negative 2, negative 2 comma negative 3, negative 3 comma negative 4, and negative 4 comma negative 5. To the right of the vertex, the line passes through 2 comma negative 1, 3 comma negative 2, 4 comma negative 3, and 5 comma negative 4.
B
Image with description A coordinate plane with a horizontal axis labeled x and a vertical axis labeled f (x). The scale on both axes ranges from negative 5 to 5 with an interval of 1 unit. An upward-opening V-shaped line has its vertex at 1 comma 0. To the left of the vertex, the line passes through 0 comma 1, negative 1 comma 2, negative 2 comma 3, negative 3 comma 4, and negative 4 comma 5. To the right of the vertex, the line passes through 2 comma 1, 3 comma 2, 4 comma 3, and 5 comma 4.
C
Image with description On a coordinate plane, a piecewise function has 2 connecting lines. The first line goes from (4 comma 5) down to (0 comma 1). The second line goes from (0 comma 1 up through (4 comma 5).
D
Image with description A coordinate plane with a horizontal axis labeled x and a vertical axis labeled f (x). The scale on both axes ranges from negative 5 to 5 with an interval of 1 unit. An inverted, downward-opening V-shaped line has its vertex at 0 comma 1. To the left of the vertical axis, the line passes through negative 1 comma 0, negative 2 comma negative 1, negative 3 comma negative 2, negative 4 comma negative 3, and negative 5 comma negative 4. To the right of the vertical axis, the line passes through 1 comma 0, 2 comma negative 1, 3 comma negative 2, 4 comma negative 3, and 5 comma negative 4.
4

Fuaad solved an absolute value inequality and expressed the solution as negative 12 is less than x comma x is less than 7 What is another way to show Fuaad’s solution?

A
left parenthesis negative 12 comma 7 right bracket
B
the union of open paren infinity close paren and open paren 7 close paren
C
start set x such that x is greater than negative 12 or x comma negative 12 or x is less than 7 end set
D
start set x such that negative 12 is less than x comma x is less than 7 end set
5

Which graph shows the solution to the inequality start absolute value x plus 3 end absolute value is greater than or equal to 2 ?

A
Image with description A number line marked as x ranges from negative 6 to 6 in intervals of 1. Closed circles are on negative 5 and negative 1 and are connected.
B
Image with description Number line extending indefinitely in both directions, indicated by arrows at each end. Solid points are marked at 1 and 5. The highlighted line extends from negative infinity to 1, and from 5 to positive infinity, with both endpoints included. This represents all numbers less than or equal to 1, or greater than or equal to 5.
C
Image with description A number line marked as x ranges from negative 6 to 6 in intervals of 1. Closed circles are on 1 and 5 and are connected.
D
Image with description Number line extending indefinitely in both directions, indicated by arrows at each end. Solid points are marked at negative 5 and negative 1. A highlighted line begins at negative 5, passes through negative 1, and continues infinitely to the left and right. This represents all real numbers on the number line, with negative 5 and negative 1 included.
6

Which of the following describes the graph of y is equal to lfloor x minus 2 rfloor ?

A
The graph has open circles on the left of each step and closed circles on the right and includes the step y is equal to negative 3 for negative 2 is less than or equal to x comma x is less than negative 1 .
B
The graph has closed circles on the left of each step and open circles on the right and includes the step y is equal to negative 4 for negative 2 is less than or equal to x comma x is less than negative 1 .
C
The graph has open circles on the left of each step and closed circles on the right and includes the step y is equal to negative 4 for negative 2 is less than or equal to x comma x is less than negative 1 .
D
The graph has closed circles on the left of each step and open circles on the right and includes the step y is equal to negative 3 for negative 2 is less than x comma x is less than or equal to negative 1 .

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