Functions and Transformations

What is the parent function for an absolute value function?

• f(x)=x³

• f(x)=x

• f(x)=IxI

• f(x)=x²

What is the parent function for a cubic function?

• f(x)=x³

• f(x)=x

• f(x)=IxI

• f(x)=x²

Describe the transformation that is applied to the parent function. 
f(x) = IxI -5

• Shifts left 5

• Shifts right 5

• Shifts up 5

• Shifts down 5

If the blue graph is the parent function, what is the equation of the red (transformed) function?

• g(x)=x³+1

• g(x)=x³-1

• g(x)=(x-1)³

• g(x)=(x+1)³

Tags

CCSS.HSF.BF.B.3

The graph shows the function f(x)=x³ in blue and another function g(x) in red.  Which could be the equation for g(x)?

• g(x) = -x³

• g(x) = x³ - 1

• g(x) = (x + 1)³

• g(x) = (x - 1)³

Tags

CCSS.HSF.BF.B.3

What is the effect on the graph of the linear parent function, f(x) = x, when f(x) is replaced by f(x- 7)? Complete the sentence by selecting the correct answers from the drop-down menus. The graph of the line ​ (a)   ​ ​ (b)   7 units.

• shifts horizontally

• up

• down

• left

• right

• shifts vertically

• vertically

• horizontally

Match the following

• The line shifted 6 units to the right.

• f(x)+3

• The line shifted 3 units up.

• f(x+6)

• The line shifted 3 units to the left.

• f(x)-6

• The line shifted 6 units down.

• f(x+3)

• The line shifted 6 units to the left.

• f(x-6)

Tags

CCSS.HSF.BF.B.3

What is the effect on the graph of the linear parent function, f(x) = x, when f(x) is replaced by f(x- 7)? Complete the sentence by selecting the correct answers from the drop-down menus. The graph of the line ​ (a)   ​ ​ (b)   7 units.

• shifts horizontally

• up

• down

• left

• right

• shifts vertically

Rewrite f(x) = 2x - 1 shifted up three units and the slope doubled (a)  

• f(x) = 5x - 2

• f(x) = 4x + 2

• f(x) = 4x + 3

• f(x) = 5x - 4