Transformation of Functions

Describe the transformation of y = f(x) for the new function
 y = f(x) - 5

• The graph of y = f(x) was shifted to the right 5 units. 

• The graph of y = f(x) was shifted to the left 5 units. 

• The graph of y = f(x) was shifted up 5 units. 

• The graph of y = f(x) was shifted down 5 units.

Tags

CCSS.HSF.BF.B.3

How did the equation shift from the parent function? y = f(x - 4)

• Shift right by 4

• Shift left by 4

• Horizontal Stretch by 4

• Vertical Stretch by 4

• Shift down by 4

Describe the transformation if y = f(x) is replaced with y = - f(x).

• f(x) has been reflected over the x-axis.

• f(x) has been reflected over the y-axis.

Tags

CCSS.HSF.BF.B.3

Describe the transformations that maps
y = g(x) to y = - g(x + 6) - 10

• Reflect over y-axis
  Shifted down 10 units
  Shifted left 6 units

• Reflect over x-axis
  Shifted up 10 units
  Shifted left 6 units

• Reflect over y-axis
  Shifted up 10 units
  Shifted right 6 units

• Reflect over x-axis
  Shifted down 10 units
  Shifted left 6 units

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

The linear parent function, f(x) = x, is transformed to g(x) = f(x) - 6. Describe the transformation. (a)  

• g(x) is shifted up 6 units

• g(x) is shifted down 6 units

• g(x) is shifted left 6 units

• g(x) is shifted right 6 units

The linear parent function, f(x) = x, is transformed to g(x) = f(x + 3). Describe the transformation. (a)  

• g(x) is shifted up 3 units

• g(x) is shifted down 3 units

• g(x) is shifted left 3 units

• g(x) is shifted right 3 units

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

Match the following

• The line shifted 6 units to the left.

• f(x+6)

• The line shifted 3 units up.

• f(x-6)

• The line shifted 3 units to the left.

• f(x+3)

• The line shifted 6 units down.

• f(x)-6

• The line shifted 6 units to the right.

• f(x)+3

Tags

CCSS.HSF.BF.B.3

• Flip

• Vertical Compression

• Same as

• Vertical Stretch

• Horizontal Stretch

• Horizontal Compression

• (-4,-1)

• (4,1)

Tags

CCSS.HSF.BF.B.3