Transformation of Functions Honors

The blue graphs is the parent function f(x)=|x|, the red must be

• g(x)=|x+2|

• g(x)=|x|+2

• g(x)=|x-2|

• g(x)=|x|-2

If the blue function is f(x)=x², then the red function must be

• g(x)=x²-5

• g(x)=x²+5

• g(x)=(x-5)²

• g(x)=(x+5)²

Use the graphs of f and g to describe the transformation from the graph of f to the graph of g.
f(x)=3x, g(x)=-f(x)

• g is a reflection on the x-axis

• g is a reflection on the y-axis

• g is a vertical stretch

• g is a horizontal stretch

Which transformation will occur if f(x) = x is replaced with f(2x)?

• Vertical stretch

• Vertical compression

• Vertical translation up by 2 units.
  Horizontal stretch

• Horizontal compression

Identify the transformation from the graph of f(x)=x² to the graph g(x)= -(x+5)² 

• shifted up five units
  reflection in x-axis

• shifted down five units
  reflection in x-axis

• shifted left 5 units
  reflection x-axis

• shifted right 5 units
  reflection x-axis

Identify the transformations. 

• horizontal shift to the left 2 and vertical stretch by a factor of 3

• horizontal shift to the right 2 and vertical stretch by a factor of 3

• horizontal shift to the right 2 and vertical shrink by a factor of 3

• horizontal shift to the left 2 and vertical shrink by a factor of 3

The original function has equation f(x).  State the transformations given the new function f(x) = ⅔(x - 7)² 

• Vertical Shrink of ⅔
  Right 7

• Horizontal Shrink of ⅔
  Left 7

• Left  ⅔
  Vertical stretch of 7

• Right ⅔
  Horizontal stretch of 7

Which transformation on f(x) = x is g(x) = -f(x)

• Reflection across the y-axis

• The slope will be less steep

• The graph will be wider

• Reflection across the x-axis.

Which equation transforms f(x) = x to a horizontal stretch by a factor of 2, a reflection over the x axis, and a shift down 4?

• f(-2x - 4)

• f(-1/2x) - 4

• -f(2x) - 4

• -f(1/2x) - 4

Describe the transformation of the graph
y = -(x - 4)³ + 5

• Up 5 and Left 4

• Reflect x-axis, Left 4, Up 5

• Reflect x-axis, Right 4, Up 5

• Right 4 and up 5