AnswersAlgebra INonlinear Functions

Practice Test Answers

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1
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Which graph shows a function with a range of all real numbers greater than or equal to negative 1 ?

A
Image with description A coordinate plane with both the axis labeled from negative 5 to 5 with increments of 1. The curve represents an absolute value function with its maximum vertex located at the coordinate points negative 2 comma 1. Moving downward from this vertex to the left, the line passes through the intersection at negative 3 comma 0, with an arrow indicating it continues downward into the third quadrant towards negative 5 comma negative 2. Moving downward to the right, the line crosses the vertical axis at a y-intercept of 0 comma negative 1 and passes through the intersections at negative 1 comma 0 and 4 comma negative 5.
B
Image with description A coordinate plane with both the axis are labeled from negative 5 to 5 with increments of 1. The curve represents an absolute value function with its minimum vertex located at the coordinate points negative 2 comma 1. Moving upward from this vertex to the left, the line passes through the intersection at negative 5 comma 4, with an arrow indicating it continues upward into the second quadrant. Moving upward to the right, the line crosses the vertical axis at a y-intercept of 0 comma 3 and passes through the intersection at 2 comma 5.
C
Image with description A coordinate plane with a V-shaped graph opening downward. The x-axis is labeled from negative 5 to 5 in increments of 1 and the y-axis is labeled from negative 5 to 5 in increments of 1. The graph has its vertex at approximately negative 1 comma negative 1. From the vertex, one ray extends downward to the left with a steep negative slope, passing through approximately negative 4 comma negative 4. A second ray extends downward to the right with a steep negative slope, passing through approximately 0 comma negative 5.
D
Image with description A coordinate plane with a V-shaped graph opening downward. The x-axis is labeled from negative 5 to 5 in increments of 1 and the y-axis is labeled from negative 5 to 5 in increments of 1. The graph has its vertex at approximately 1 comma 2. From the vertex, one ray extends downward to the left with a steep negative slope, ending with an arrow near negative 4 comma negative 5. A second ray extends downward to the right with a steep negative slope, ending with an arrow near 4 comma negative 4.
2
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If g of x is equal to 2 lfloor x rfloor minus 1 , what is g of negative 2 point 3 ?

A
negative 4
B
negative 3
C
negative 5
D
negative 7
3

Which describes the range of the parent absolute value function?

A
start set y such that y is less than or equal to 0 end set
B
start set y such that y is greater than or equal to 0 end set
C
start set y such that y is a real number end set
D
start set y such that y is an integer end set
4

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 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.
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 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.
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 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.
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 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.
5

The step function g of x is defined as shown. g of x is equal to negative 3 when x is less than or equal to 0; g of x is equal to 2 when 0 is less than x comma x is less than or equal to 4; g of x is equal to 5 when 4 is less than x comma x is less than or equal to 10 What is the range of g of x ?

A
start set negative 3 comma 2 comma 5 end set
B
0 is less than or equal to g of x comma g of x is less than or equal to 10
C
negative 3 is less than or equal to g of x comma g of x is less than or equal to 5
D
start set 0 comma 4 comma 10 end set
6

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.
7

What is the vertex of the graph of f of x is equal to start absolute value x plus 3 end absolute value plus 7 ?

A
7 comma negative 3
B
7 comma 3
C
3 comma 7
D
negative 3 comma 7
8

The graph of f of x is equal to absolute value of x is reflected across the x -axis and translated to the right 6 units. Which statement about the domain and range of each function is correct?

A
The range of the transformed function is the same as the parent function, but the domains of the functions are different.
B
Neither the domain nor the range of the transformed function are the same as those of the parent function.
C
Both the domain and range of the transformed function are the same as those of the parent function.
D
The domain of the transformed function is the same as the parent function, but the ranges of the functions are different.

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