AnswersAlgebra 1Absolute Value Functions and Translations

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On each coordinate plane, the parent function f of x is equal to absolute value of x is represented by a dashed line and a translation is represented by a solid line. Which graph represents the translation g of x is equal to absolute value of x minus 4 as a solid line?

A
Image with description A coordinate plane with two V-shaped graphs. The x-axis and y-axis are labeled from negative 6 to 6 in increments of 1. The first graph is a dashed line labeled f of x equals absolute value of x, opens upward with its vertex at the origin 0 comma 0, and passes through the points negative 1 comma 1 and 1 comma 1. The second graph is a solid line, opens upward with its vertex at negative 4 comma 0, and passes through the points negative 6 comma 2 and negative 2 comma 2.
B
Image with description A coordinate plane with two V-shaped graphs. The x-axis and y-axis are labeled from negative 6 to 6 in increments of 1. The first graph is a dashed line labeled f of x equals absolute value of x, opens upward with its vertex at the origin 0 comma 0, and passes through the points negative 1 comma 1 and 1 comma 1. The second graph is a solid line, opens upward with its vertex at 0 comma negative 4, and passes through the points negative 4 comma 0 and 4 comma 0.
C
Image with description A coordinate plane with two V-shaped graphs. The x-axis and y-axis are labeled from negative 6 to 6 in increments of 1. The first graph is a dashed line labeled f of x equals absolute value of x, opens upward with its vertex at the origin 0 comma 0, and passes through the points negative 1 comma 1 and 1 comma 1. The second graph is a solid line, opens upward with its vertex at 4 comma 0, and passes through the points 2 comma 2 and 6 comma 2.
D
Image with description A coordinate plane with two V-shaped graphs. The x-axis and y-axis are labeled from negative 6 to 6 in increments of 1. The first graph is a dashed line labeled f of x equals absolute value of x, opens upward with its vertex at the origin 0 comma 0, and passes through the points negative 1 comma 1 and 1 comma 1. The second graph is a solid line, opens upward with its vertex at 0 comma 4, and passes through the points negative 2 comma 6 and 2 comma 6.
2
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Which functions have a vertex with an x -value of 0 ? Choose three correct answers.

A
f of x is equal to start absolute value x plus 3 end absolute value
B
f of x is equal to absolute value of x plus 3
C
f of x is equal to absolute value of x
D
f of x is equal to start absolute value x plus 3 end absolute value minus 6
E
f of x is equal to absolute value of x minus 6
3

What is the range of the function g of x is equal to start absolute value x minus 12 end absolute value minus 2 ?

A
start set y such that y is greater than or equal to 12 end set
B
start set y such that y is greater than negative 2 end set
C
start set y such that y is greater than 12 end set
D
start set y such that y is greater than or equal to negative 2 end set
4

What is the vertex of the graph of f of x is equal to start absolute value x plus 5 end absolute value minus 6 ?

A
negative 5 comma negative 6
B
5 comma negative 6
C
negative 6 comma negative 5
D
negative 6 comma 5
5

The graph of f of x is equal to absolute value of x is transformed to g of x is equal to start absolute value x plus 1 end absolute value minus 7 On which interval is the function decreasing?

A
open paren negative infinity comma negative 7 close paren
B
open paren negative infinity comma 1 close paren
C
open paren negative infinity comma 7 close paren
D
open paren negative infinity comma negative 1 close paren
6

The graph of f of x is equal to absolute value of x is translated 6 units to the right and 2 units up to form a new function. Which statement about the range of both functions is true?

A
The range changes from start set y such that y is greater than or equal to 0 end set to start set y such that y is greater than or equal to 6 end set .
B
The range is the same for both functions: start set y such that y is greater than or equal to 0 end set .
C
The range is the same for both functions: start set y such that y is a real number end set .
D
The range changes from start set y such that y is greater than or equal to 0 end set to start set y such that y is greater than or equal to 2 end set .
7

Which graph represents the function h of x is equal to absolute value of x plus 0 point 5 ?

A
Image with description A coordinate plane with a V-shaped graph. The x and y axes are labeled from negative 3 to 3 in increments of 1. The graph opens upward with a vertex at negative 0.5 comma 0, with one ray extending toward the upper left and the other extending toward the upper right from the vertex.
B
Image with description A coordinate plane with a V-shaped graph. The x and y axes are labeled from negative 3 to 3 in increments of 1. The graph opens upward with a vertex at negative 0.5 comma 0, with one ray extending toward the upper left and the other extending toward the upper right from the vertex.
C
Image with description A coordinate plane with a V-shaped graph. The x and y axes are labeled from negative 3 to 3 in increments of 1. The graph opens upward with a vertex at negative 1.5 comma 0, with one ray extending toward the upper left and the other extending toward the upper right from the vertex.
D
Image with description A coordinate plane with a V-shaped graph. The x and y axes are labeled from negative 3 to 3 in increments of 1. The graph opens upward with a vertex at 0 comma 1.5, and passes through the points negative 1 comma, 2.5, and 1 comma 2.5.
8

Over which interval is the graph of the parent absolute value function f of x is equal to absolute value of x decreasing?

A
open paren negative infinity comma 0 close paren
B
open paren negative 6 comma 0 close paren
C
open paren negative infinity comma infinity close paren
D
open paren 0 comma infinity close paren
9

On each coordinate plane, the parent function f of x is equal to absolute value of x is represented by a dashed line and a translation is represented by a solid line. Which graph represents the translation g of x is equal to start absolute value x plus 2 end absolute value as a solid line?

A
Image with description " A coordinate plane with two V-shaped graphs. The horizontal axis and vertical axis are labeled from negative 6 to 6 in increments of 1. The first graph is a solid line labeled f of x equals absolute value of x, opens downward with its vertex at the origin 0 comma 0, and passes through the points negative 1 comma negative 1 and 1 comma negative 1. The second graph is a dashed line, opens downward with its vertex at 1 comma 0, and passes through the points negative 1 comma negative 2 and 3 comma negative 2."
B
Image with description A coordinate plane with two V-shaped graphs. The horizontal axis and vertical axis are labeled from negative 6 to 6 in increments of 1. The first graph is a solid line labeled f of x equals absolute value of x, opens upward with its vertex at the origin 0 comma 0, and passes through the points negative 1 comma 1 and 1 comma 1. The second graph is a dashed line, opens upward with its vertex at 1 comma 0, and passes through the points negative 1 comma 2 and 3 comma 2.
C
Image with description A coordinate plane with two V-shaped graphs. The horizontal axis and vertical axis are labeled from negative 6 to 6 in increments of 1. The first graph is a solid line labeled f of x equals absolute value of x, opens downward with its vertex at the origin 0 comma 0, and passes through the points negative 1 comma negative 1 and 1 comma negative 1. The second graph is a dashed line, opens downward with its vertex at 1 comma 0, and passes through the points negative 1 comma negative 2 and 3 comma negative 2.
D
Image with description A coordinate plane with two V-shaped curves. The x-axis is labeled from negative 6 to 6 and the y-axis is labeled from negative 6 to 6. A dashed V-shaped curve with its vertex at the origin 0 comma 0 opens upward with slopes of 1 and negative 1. A solid V-shaped curve with its vertex at 0 comma 2 opens upward with slopes of 1 and negative 1.
10

Which graph represents the function r of x is equal to start absolute value x minus 2 end absolute value minus 1 ?

A
Image with description A coordinate plane with a V-shaped graph opening upward. The x-axis and y-axis are labeled from negative 6 to 6 in increments of 1. The graph has its vertex at negative 1 comma negative 2, ascends to the left passing through negative 5 comma 2, and ascends to the right passing through 4 comma 5.
B
Image with description A coordinate plane with a V-shaped graph opening upward. The x-axis and y-axis are labeled from negative 6 to 6 in increments of 1. The graph has its vertex at negative 2 comma 0, ascends to the left passing through negative 5 comma 3, and ascends to the right passing through 3 comma 5.
C
Image with description A coordinate plane with a V-shaped graph opening upward. The x-axis and y-axis are labeled from negative 6 to 6 in increments of 1. The graph has its vertex at 1 comma 0, ascends to the left passing through negative 4 comma 5, and ascends to the right passing through 5 comma 4.
D
Image without description

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