AnswersAlgebraic ReasoningAbsolute Value Functions and Translations

Absolute Value Functions and Translations — Quiz Answers

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21
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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 (1, negative 2).
B
Image with description On a coordinate plane, an absolute value graph has a vertex at (2, negative 1).
C
Image with description On a coordinate plane, an absolute value graph has a vertex at (negative 1, negative 2).
D
Image without description
22
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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 negative 1 close paren
C
open paren negative infinity comma 7 close paren
D
open paren negative infinity comma 1 close paren
23

What is the vertex of the graph of g of x is equal to start absolute value x minus 8 end absolute value plus 6 ?

A
negative 8 comma 6
B
6 comma negative 8
C
8 comma 6
D
6 comma 8
24

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 0 comma infinity close paren
C
open paren negative 6 comma 0 close paren
D
open paren negative infinity comma infinity close paren
25

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
5 comma negative 6
B
negative 6 comma negative 5
C
negative 5 comma negative 6
D
negative 6 comma 5
26

The graph of the parent absolute value function f⁡(x)=|x| includes vertex V⁡(0,0) and points T⁡(−2,2) and W⁡(6,6) The graph of the absolute value function g⁡(x)=|x+7|−3 can be obtained by translating the graph of f⁡(x) Plot V^′ , T^′ , and W^′ , the images of V , T , and W after the graph of f⁡(x) is translated. Plot each point on the coordinate grid.

Answer:

point; -7; -3; -9; -1; 3

27

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 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 .
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 2 end set .
D
The range is the same for both functions: start set y such that y is a real number end set .
28

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 (4, 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 (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 (0, 4).
29

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 (4, 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 4).
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, 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 (negative 4, 0).
30

The graph shows the function f of x is equal to start absolute value x minus h end absolute value plus k What is the value of k ?

A
k is equal to 1
B
k is equal to negative 1
C
k is equal to 2 point 5
D
k is equal to negative 2 point 5
31

The graph of h of x is equal to start absolute value x minus 10 end absolute value plus 6 is shown. On which interval is this graph increasing?

A
open paren negative infinity comma 10 close paren
B
open paren 6 comma infinity close paren
C
open paren 10 comma infinity close paren
D
open paren negative infinity comma 6 close paren
32

Which equation represents the function graphed on the coordinate plane?

A
g of x is equal to start absolute value x plus 4 end absolute value minus 10
B
g of x is equal to start absolute value x minus 4 end absolute value minus 10
C
g of x is equal to start absolute value x minus 10 end absolute value plus 4
D
g of x is equal to start absolute value x plus 10 end absolute value minus 4

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