Absolute Value Parent Functions and Translations

Complete the chart by labeling the rules with the resulting transformations

a

b

c

h

g

e

f

vertical stretch (narrower)

vertical compression (wider)

reflect across the x-axis

shift down "h" units

shift right "k" units

shift left "h" units

shift up "k" units

shift right "h" units

reflect across the y-axis

shift down "k" units

Apply a horizontal translation of -3 to the absolute value function y = |x|.

• y = |x+3|

• y = |x-3|

• y = |x| - 3

• y = |x| + 3

Apply a vertical translation of +5 to the absolute value function y = |x|.

• y = |x| + 5

• y = |x - 5|

• y = |x| - 5

• y = |x + 5|

Apply a horizontal translation of +2 to the absolute value function y = |x|.

• y = |x-2|

• y = |x+2|

• y = |x| + 2

• y = |x-2| + 2

Graph the absolute value parent function y = |x|.

• V-shaped graph with the vertex at the origin

• Exponential growth graph

• Horizontal line passing through the origin

• U-shaped graph with the vertex at the origin

Tags

CCSS.HSF-IF.C.7D

Explain the understanding of translations of absolute value functions.

• Translations involve shifting the graph horizontally or vertically.

• Translations involve reflecting the graph

• Translations involve rotating the graph

• Translations involve stretching the graph

Apply a vertical translation of -2 to the absolute value function y = |x|.

• y = |x| * 2

• y = |x| / 2

• y = |x| - 2

• y = |x| + 2

Solve the equation |3x + 4| = 10.

• x = 2 or x = -14/3

• x = 3 or x = -4

• x = 1 or x = -8

• x = 6 or x = -1

Graph the absolute value function y = |x+2|.

• V-shaped graph shifted 2 units to the left

• V-shaped graph shifted 2 units to the right

• U-shaped graph shifted 2 units to the left

• U-shaped graph shifted 2 units to the right

Tags

CCSS.HSF-IF.C.7D

What is the equation of the graph below?

• f(x ) = I x + 4 I + 2

• f(x ) = -I x - 4 I + 2

• f(x ) = I x - 4 I + 2

• f(x ) = -I x + 4 I + 2

Tags

CCSS.HSF-IF.C.7D