What is the domain of the absolute value function?

[ 4 , ∞ ) \left[4,\ \infty\right) [ 4 , ∞ )

f ( x ) = ∣ x − 2 ∣ + 4 f\left(x\right)=\left|x-2\right|+4 f ( x ) = ∣ x − 2 ∣ + 4 was translated 5 units right and 1 unit down. What is the new function rule?

f ( x ) = ∣ x − 7 ∣ + 3 f\left(x\right)=\left|x-7\right|+3 f ( x ) = ∣ x − 7 ∣ + 3

f ( x ) = ∣ x − 7 ∣ + 5 f\left(x\right)=\left|x-7\right|+5 f ( x ) = ∣ x − 7 ∣ + 5

f ( x ) = ∣ x + 3 ∣ + 3 f\left(x\right)=\left|x+3\right|+3 f ( x ) = ∣ x + 3 ∣ + 3

f ( x ) = ∣ x + 3 ∣ + 5 f\left(x\right)=\left|x+3\right|+5 f ( x ) = ∣ x + 3 ∣ + 5

Write the inequality for the absolute function.

f ( x ) < − ∣ x − 2 ∣ + 3 f\left(x\right)<-\left|x-2\right|+3 f ( x ) < − ∣ x − 2 ∣ + 3

f ( x ) < ∣ − ( x − 2 ) ∣ + 3 f\left(x\right)<\left|-\left(x-2\right)\right|+3 f ( x ) < ∣ − ( x − 2 ) ∣ + 3

f ( x ) ≤ − ∣ x − 3 ∣ + 2 f\left(x\right)\le-\left|x-3\right|+2 f ( x ) ≤ − ∣ x − 3 ∣ + 2

f ( x ) > − ∣ x − 2 ∣ + 3 f\left(x\right)>-\left|x-2\right|+3 f ( x ) > − ∣ x − 2 ∣ + 3

Write the inequality for the absolute value function.

f ( x ) ≥ ∣ x + 4 ∣ − 1 f\left(x\right)\ge\left|x+4\right|-1 f ( x ) ≥ ∣ x + 4 ∣ − 1

f ( x ) ≤ ∣ x + 4 ∣ − 1 f\left(x\right)\le\left|x+4\right|-1 f ( x ) ≤ ∣ x + 4 ∣ − 1

f ( x ) ≥ ∣ x − 4 ∣ − 1 f\left(x\right)\ge\left|x-4\right|-1 f ( x ) ≥ ∣ x − 4 ∣ − 1

f ( x ) = − ∣ x + 3 ∣ − 4 f\left(x\right)=-\left|x+3\right|-4 f ( x ) = − ∣ x + 3 ∣ − 4 was translated 6 units left and 2 units up. What is the new function rule?

f ( x ) = − ∣ x + 9 ∣ − 2 f\left(x\right)=-\left|x+9\right|-2 f ( x ) = − ∣ x + 9 ∣ − 2

f ( x ) = − ∣ x + 9 ∣ + 2 f\left(x\right)=-\left|x+9\right|+2 f ( x ) = − ∣ x + 9 ∣ + 2

f ( x ) = − ∣ x − 3 ∣ − 2 f\left(x\right)=-\left|x-3\right|-2 f ( x ) = − ∣ x − 3 ∣ − 2

f ( x ) = − ∣ x − 3 ∣ − 6 f\left(x\right)=-\left|x-3\right|-6 f ( x ) = − ∣ x − 3 ∣ − 6

Which equation describes a reflection across the x-axis, a translation of 7 units right and 5 units down?

f ( x ) = − ∣ x − 7 ∣ − 5 f\left(x\right)=-\left|x-7\right|-5 f ( x ) = − ∣ x − 7 ∣ − 5

f ( x ) = − ∣ x + 7 ∣ − 5 f\left(x\right)=-\left|x+7\right|-5 f ( x ) = − ∣ x + 7 ∣ − 5

f ( x ) = ∣ x − 7 ∣ − 5 f\left(x\right)=\left|x-7\right|-5 f ( x ) = ∣ x − 7 ∣ − 5

f ( x ) = − ∣ x − 5 ∣ − 7 f\left(x\right)=-\left|x-5\right|-7 f ( x ) = − ∣ x − 5 ∣ − 7

Which of the following functions has a line of symmetry at x = -2?

f ( x ) = ∣ x + 2 ∣ f(x)=|x+2| f ( x ) = ∣ x + 2 ∣

f ( x ) = ∣ x ∣ + 2 f(x)=|x|+2 f ( x ) = ∣ x ∣ + 2

f ( x ) = ∣ x − 2 ∣ f(x)=|x-2| f ( x ) = ∣ x − 2 ∣

f ( x ) = ∣ x ∣ − 2 f(x)=|x|-2 f ( x ) = ∣ x ∣ − 2

What is the range of the function h ( x ) = − 2 ∣ x + 10 ∣ − 7 h(x)=-2|x+10|-7 h ( x ) = − 2 ∣ x + 1 0 ∣ − 7 ?

( − ∞ , − 7 ] (-∞,-7] ( − ∞ , − 7 ]

[ − 10 , ∞ ) [-10,∞) [ − 1 0 , ∞ )

[ 10 , ∞ ) [10,\ ∞) [ 1 0 , ∞ )

[ − 7 , ∞ ) [-7,∞) [ − 7 , ∞ )

Select all that apply. (May have more than one correct answer) f(x) = |x - 6| + 2

Horizontal translation right 6 units

Vertical translation up 2 units

Horizontal translation left 6 units

Vertical translation down 2 units

Determine the transformation

Stretch by factor of 2, right 3

Choose all functions that show a reflection over the y-axis

f ( x ) = ∣ − ( x + 5 ) ∣ f\left(x\right)=\left|-\left(x+5\right)\right| f ( x ) = ∣ − ( x + 5 ) ∣

f ( x ) = ∣ − ( x − 1 ) ∣ − 4 f\left(x\right)=\left|-\left(x-1\right)\right|-4 f ( x ) = ∣ − ( x − 1 ) ∣ − 4

f ( x ) = − ∣ x ∣ + 5 f\left(x\right)=-\left|x\right|+5 f ( x ) = − ∣ x ∣ + 5

f ( x ) = − ∣ x + 8 ∣ f\left(x\right)=-\left|x+8\right| f ( x ) = − ∣ x + 8 ∣

f ( x ) = ∣ x − 6 ∣ − 2 f\left(x\right)=\left|x-6\right|-2 f ( x ) = ∣ x − 6 ∣ − 2

Unit 3A Review - Absolute Value Functions

Authored by Judith M Alvarado

Mathematics

9th - 12th Grade

CCSS covered

Used 80+ times

Unit 3A Review - Absolute Value Functions

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51 questions

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MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Which function is graphed?

f(x) = 2|x + 2| -4

f(x) = 2|x - 4| + 2

f(x) = |x + 2| - 4

f(x) = -2|x - 4|

Tags

CCSS.HSF-IF.C.7D

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Which function is graphed?

f(x) = 2|x - 5|

f(x) = |x - 5|

f(x) = |x - 5| + 5

f(x) = |x| + 5

Tags

CCSS.HSF-IF.C.7D

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Describe the transformation from the Absolute Value Parent Function.

Shift up 4 units

Shift down 4 units

Shift left 4 units

Shift right 4 units

Tags

CCSS.HSF.BF.B.3

CCSS.HSG.CO.A.2

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

What is the range of the absolute value function?

$\left(-\infty,\ \infty\right)$

$\left[3,\ \infty\right)$

$\left[0,\infty\right)$

$\left(-\infty,\ 3\right]$ (-infinity, 3]

Tags

CCSS.8.F.A.1

CCSS.HSF.IF.B.5

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

What is the equation of the graph below?

$f\left(x\right)=\left|x+2\right|$

$f\left(x\right)=\left|x+2\right|+2$

$f\left(x\right)=\left|x-2\right|+2$

$f\left(x\right)=\left|x-2\right|$

Tags

CCSS.HSF-IF.C.7D

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Describe the transformation of the equation below from the parent function of f(x) = IxI to $g\left(x\right)=\left|x+2\right|-5$

Left 2 up 5

Right 2 up 5

Left 2 down 5

Right 2 down 5

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

What translations have occurred?

left 1, up 5

left 1, down 5

right 1, down 5

right 1, up 5

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

What is the vertex of the following function? (Try not to graph) $f\left(x\right)=-4\left|x+2\right|+5$

(-4, 2)

(-2, 5)

(-4, -2)

(2, 5)

Tags

CCSS.HSF-IF.C.7D

10.

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

What is the vertex of the following function? (Try not to graph)

$f\left(x\right)=4\left|x-3\right|+1$

(3,1)

(-3,1)

(1,-3)

(0,0)

Tags

CCSS.HSF-IF.C.7D

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Unit 3A Review - Absolute Value Functions

Which function is graphed?

Which function is graphed?

Describe the transformation from the Absolute Value Parent Function.

What is the range of the absolute value function?

What is the equation of the graph below?

Describe the transformation of the equation below from the parent function of f(x) = IxI to g(x)=∣x+2∣−5g\left(x\right)=\left|x+2\right|-5g(x)=∣x+2∣−5

What translations have occurred?

Which of the following describes the horizontal and vertical translations of the following functions:f(x) = |x + 4| - 9

What is the vertex of the following function? (Try not to graph) f(x)=−4∣x+2∣+5f\left(x\right)=-4\left|x+2\right|+5f(x)=−4∣x+2∣+5

What is the vertex of the following function? (Try not to graph) f(x)=4∣x−3∣+1f\left(x\right)=4\left|x-3\right|+1f(x)=4∣x−3∣+1

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Describe the transformation of the equation below from the parent function of f(x) = IxI to $g\left(x\right)=\left|x+2\right|-5$

Which of the following describes the horizontal and vertical translations of the following functions:
f(x) = |x + 4| - 9

What is the vertex of the following function? (Try not to graph) $f\left(x\right)=-4\left|x+2\right|+5$

What is the vertex of the following function? (Try not to graph)

$f\left(x\right)=4\left|x-3\right|+1$