AnswersAlgebraic ReasoningAbsolute Value Functions and Translations

Absolute Value Functions and Translations — Quiz Answers

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1
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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 negative 2 end set
B
start set y such that y is greater than or equal to 12 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 12 end set
2
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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 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 (negative 2, 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 2).
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).
3

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 (negative 1, negative 2).
C
Image without description
D
Image with description On a coordinate plane, an absolute value graph has a vertex at (2, negative 1).
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 6 comma negative 5
B
5 comma negative 6
C
negative 6 comma 5
D
negative 5 comma negative 6
5

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 (negative 1.5, 0).
B
Image with description On a coordinate plane, an absolute value graph has a vertex at (0, 1.5).
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 0.5, 0).
6

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 7 close paren
D
open paren negative infinity comma negative 1 close paren
7

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 infinity comma infinity close paren
C
open paren negative 6 comma 0 close paren
D
open paren 0 comma infinity close paren
8

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 .
9

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).
10

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 negative 2 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 or equal to 12 end set
D
start set y such that y is greater than 12 end set
11

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 infinity 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 0 close paren
12

The graph of g of x is equal to start absolute value x minus h end absolute value plus k is shown on the coordinate grid. What must be true about the signs of h and k ?

A
h must be positive and k must be negative.
B
Both h and k must be negative.
C
h must be negative and k must be positive.
D
Both h and k must be positive.
13

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, negative 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 (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, 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).
14

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 h ?

A
h is equal to 1 point 5
B
h is equal to negative 1 point 5
C
h is equal to negative 3 point 5
D
h is equal to 3 point 5
15

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 (negative 0.5, 0).
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 1.5, 0).
D
Image with description On a coordinate plane, an absolute value graph has a vertex at (0, 1.5).
16

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 (negative 1.5, 0).
B
Image with description On a coordinate plane, an absolute value graph has a vertex at (0, 1.5).
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 0.5, 0).
17

What is the vertex of the graph of y=|x−11|−3 ? Enter your answer in the box.

Answer:

(11,-3)

18

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 (negative 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, 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 (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, negative 2).
19

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 (0, negative 2).
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, 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 (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 (negative 2, 0).
20

Which graph represents the function f of x is equal to start absolute value x plus 3 end absolute value ?

A
Image with description On a coordinate plane, an absolute value graph has a vertex at (3, 0).
B
Image with description On a coordinate plane, an absolute value graph has a vertex at (0, 3).
C
Image with description On a coordinate plane, an absolute value graph has a vertex at (negative 3, 0).
D
Image with description On a coordinate plane, an absolute value graph has a vertex at (0, negative 3).

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