A1 5-4 Transformations of Piecewise Defined Functions

A1 5-4 Transformations of Piecewise Functions

​ESSENTIAL QUESTION:

How do the constants of affect the graphs of piecewise-defined functions?​

PARENT FUNCTION

of an absolute value function​

Parameters a, h, k​

​

a- slope

h-left or right

k-up or down

​

(this formula will work with all types of polynomial graphs! just change the grouping symbols)​

​

Parameters of the Absolute Value Function:

• a Compresses or stretches the graph vertically (Graph will Push TO and Pull AWAY from the X-axis)

• h Translates the graph of the absolute value function either to the left (+h) or right (-h) !

• k Translates the graph of the absolute value function either to the up (+k) or down (-k) !

Multiple Select

Select all that apply. (May have more than one correct answer)

f(x) = |x - 6| + 2

• Horizontal translation right 6 units

• Horizontal translation left 6 units

• Vertical translation up 2 units

• Vertical translation down 2 units

Multiple Choice

What is the value of h?

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

• -4

• -2

• 4

• 2

Open Ended

What is the value of k?

f(x) = 4|x +2| - 3

Okay, let's take a look at this graph!

Multiple Choice

Which function defines the graph?

• f(x) = |x - 4| + 3

• f(x) = |x - 3| + 4

• f(x) = |-x + 4| + 3

• f(x) = |x + 4| + 3

Multiple Select

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

Multiple Choice

Write an absolute value function given the following transformations:

Vertical Stretch of 2

Horizontal shift left 1 unit

Vertical shift down 9 units

• f(x) = |2x + 1| - 9

• f(x) = |2x - 1| - 9

• f(x) = 2|x + 1| - 9

• f(x) = 2|x - 1| - 9

Multiple Select

What is the equation of the graph below?

• y = - | x + 2| + 4

• y = | x - 2| - 4

• y = - | x - 2| + 4

• y = | x - 2 | + 4

Open Ended

Describe in words how the graph transformed.

Poll

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