Absolute Value Parent Functions and Translations

Identify the parent function of absolute value.

• y = |x|

• y = x^2

• y = √x

• y = x^3

Apply a vertical translation of +3 to the absolute value function y = |x|.

• y = |x - 3|

• y = |x| + 3

• y = |x| - 3

• y = |x + 3|

Apply a horizontal translation of +4 to the absolute value function y = |x|.

• y = |x-4|

• y = |x+4|

• y = |x| + 4

• y = |x-4| + 4

Solve the equation |2x - 5| = 7.

• x = 6 or x = -1

• x = 1 or x = -8

• x = 3 or x = -4

• x = 10 or x = -3

Which function defines the graph?

• f(x) = -2|x - 3| + 4

• f(x) = -2|x - 4| + 3

• f(x) = -|2x + 3| + 4

• f(x) = -|2x - 3| + 4

Tags

CCSS.HSF-IF.C.7D

Describe how the following function compares

to the parent function f(x) = |x|

f(x) = -|x − 4|

• shifted right 4 units

• reflected over x-axis

• shifted left 4 units

• shifted up 4 units

• shifted down 4 units

Which graph shows y=|x−2|+3

• A

• B

• C

• D

Tags

CCSS.HSF-IF.C.7D

The blue graph is $y=\left|x\right|$
Which of the following could be the equation of the red graph?

Write the new function for the transformation: Vertically stretched by a factor of 5, then translated 1 unit left.

f(x) = ​ (a)   | x​ (b)   |

• 5

• + 1

• -5

• − 1

Describe how the following function compares to the parent function for f(x) = |x| - 3.

• shift down 3 units

• shift up 3 units

• shift left 3 units

• shift right 3 unitis

• flip over the x-axis

• flip over the y-axis

• vertical stretch by a factor of 3

• vertical compression by a factor of ⅓