AnswersMathematics IIAbsolute Value Functions and Translations

Absolute Value Functions and Translations — Quiz Answers

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1
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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 6 comma 0 close paren
B
open paren negative infinity comma infinity close paren
C
open paren negative infinity comma 0 close paren
D
open paren 0 comma infinity close paren
2
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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 6 comma negative 5
B
negative 6 comma 5
C
5 comma negative 6
D
negative 5 comma negative 6
3

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

A
Image with description On a coordinate plane, an absolute value graph has a vertex at (0, 1.5).
B
Image with description On a coordinate plane, an absolute value graph has a vertex at (negative 0.5, 0).
C
Image with description On a coordinate plane, an absolute value graph has a vertex at (negative 0.5, 0).
D
Image with description On a coordinate plane, an absolute value graph has a vertex at (negative 1.5, 0).
4

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 On a coordinate plane, a dashed line absolute value graph has a vertex at (0, 0). A solid line absolute value graph has a vertex at (2, 0).
B
Image with description On a coordinate plane, a dashed line absolute value graph has a vertex at (0, 0). A solid line absolute value graph has a vertex at (0, negative 2).
C
Image with description On a coordinate plane, a dashed line absolute value graph has a vertex at (0, 0). A solid line absolute value graph has a vertex at (negative 2, 0).
D
Image with description On a coordinate plane, a dashed line absolute value graph has a vertex at (0, 0). A solid line absolute value graph has a vertex at (0, 2).
5

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 On a coordinate plane, an absolute value graph has a vertex at (2, negative 1).
B
Image without description
C
Image with description On a coordinate plane, an absolute value graph has a vertex at (negative 1, negative 2).
D
Image with description On a coordinate plane, an absolute value graph has a vertex at (1, negative 2).
6

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 12 end set
B
start set y such that y is greater than or equal to negative 2 end set
C
start set y such that y is greater than negative 2 end set
D
start set y such that y is greater than or equal to 12 end set
7

Which functions have a vertex with an x -value of 0 ? Choose three correct answers.

A
f of x is equal to absolute value of x
B
f of x is equal to absolute value of x minus 6
C
f of x is equal to absolute value of x plus 3
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 start absolute value x plus 3 end absolute value
8

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 7 close paren
B
open paren negative infinity comma 1 close paren
C
open paren negative infinity comma negative 1 close paren
D
open paren negative infinity comma negative 7 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 absolute value of x minus 4 as a solid line?

A
Image with description On a coordinate plane, a dashed line absolute value graph has a vertex at (0, 0). A solid line absolute value graph has a vertex at (0, 4).
B
Image with description On a coordinate plane, a dashed line absolute value graph has a vertex at (0, 0). A solid line absolute value graph has a vertex at (negative 4, 0).
C
Image with description On a coordinate plane, a dashed line absolute value graph has a vertex at (0, 0). A solid line absolute value graph has a vertex at (0, negative 4).
D
Image with description On a coordinate plane, a dashed line absolute value graph has a vertex at (0, 0). A solid line absolute value graph has a vertex at (4, 0).
10

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 is the same for both functions: start set y such that y is greater than or equal to 0 end set .
B
The range is the same for both functions: start set y such that y is a real number end set .
C
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 .
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 .

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