Transformations of Functions Graphs

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

Use the graphs of f and g to describe the transformation from the graph of f to the graph of g.

• The graph of g is a vertical translation 2 units up of the graph of f

• The graph of f is a horizontal translation two units left of g

• The graph of g is a vertical stretch by a factor of 2 of the graph of f

• The graph of g is a reflection of the graph of f

Use the graphs of f and g to describe the transformation from the graph of f to the graph of g.

• The graph of g is a vertical translation 4 units up from the graph f

• The graph of g is a horizontal translation of the graph of f, 4 units right

• The graph of g is a horizontal translation of the graph of f, 4 units left

• The graph of g is a vertical stretch of the graph of f, by a factor of 7

If f(x) = x³ is changed to f(x) = - (x + 3)³ + 2, how is the graph transformed?

Shape Change: ​ (a)  

Horizontal Change ​ (b)  

Vertical Change: ​ (c)  

Parent Function: ​ (d)  

• Flip

• Vertical Stretch

• Horizontal Stretch

• Left 3

• Right 3

• Right 2

• Up 2

• Down 2

• Polynomial: Cubic

• Quadratic

Tags

CCSS.HSF.BF.B.3

What transformations occurred to get f(x), the red graph, to become g(x), the blue graph?

• horizontal shift down and vertical shift left

• horizontal shift left and vertical shift down

• horizontal shift right and vertical shift up

• horizontal shift up and vertical shift right

What are the transformations of this functions compared to the parent function?

• Shifted down 2

• Shifted up 2

• Shifted left 2

• Shifted right 2

Tags

CCSS.HSF.BF.B.3

A student graphed f(x) = x + 1 and h(x) =f(x - 7) on the same graph. Which statement describes the graphs of f and h?​

The graph of f(x) ​ (a)   to create the graph of h.

• is shifted right 7 units

• is shifted up 7 units

• is shifted left 7 units

• is shifted down 7 units

• F

• G

• H

• J

• Flip

• Vertical Compression

• Same as

• Vertical Stretch

• Horizontal Stretch

• Horizontal Compression

• (-4,-1)

• (4,1)

Tags

CCSS.HSF.BF.B.3