Transformations of Functions

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

Tags

CCSS.HSF.BF.B.3

CCSS.HSG.CO.A.2

CCSS.HSG.CO.A.4

CCSS.HSG.CO.A.5

Use the graphs of f and g to describe the transformation from the graph of f to the graph of g.
f(x)=-x+4, g(x)=2f(x)

• g is a vertical shrink by a factor of 2
• g is a horizontal stretch by a factor of 2
• g is a vertical stretch by a factor of 2
• g is a reflection across the y-axis

Tags

CCSS.HSF.BF.B.3

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

Tags

CCSS.HSF.BF.B.3

CCSS.HSG.CO.A.2

If the blue is f(x)=x^2, the red must be

• g(x)=(x+3)²
• g(x)=(x-3)²
• g(x)=x²+3
• g(x)=x²-2

Tags

CCSS.HSA.CED.A.2

CCSS.HSA.REI.D.10

CCSS.HSA.REI.D.11

What is the equation of the quadratic function obtained from vertically stretching the parent function by a factor of 2 and then vertically shifting up 3 units?

• f(x)= 2(x-3)²
• f(x)= 2(x+3)²
• f(x)= 2x²+3
• f(x)= (x-2)²+3

Tags

CCSS.HSF.BF.B.3

If the blue graph is f(x) (the original function) and the red graph is the transformation, what is the equation of the red graph?

• -f(x)
• f(-x)
• f^-1(x)
• f(2x)

Tags

CCSS.HSF.BF.B.3

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

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

Tags

CCSS.HSF.BF.B.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

Tags

CCSS.HSF.BF.B.3

CCSS.HSG.CO.A.2

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 blue function is the original function f(x) = x³.  Which of the following is the correct equation for the red function, g(x)?

• g(x)=x³+1
• g(x)=x³-1
• g(x)=(x-1)³
• g(x)=(x+1)³

Tags

CCSS.HSF.BF.B.3