5.6: Transformations of Polynomials

What are the following transformations?
- f(x+2)

• reflection over the y axis and 2 units to the right
• reflection over the x axis and 2 units right
• reflection over the y axis and 2 units left
• reflection over the x axis and 2 units left

Tags

CCSS.HSF.BF.B.3

CCSS.HSG.CO.A.2

What are the following transformations:
f(-x) - 4

• reflection over the x axis and 4 units right
• reflection over the x axis and 4 units down
• reflection over the y axis and 4 units right
• reflection over the y axis and 4 units down

Tags

CCSS.HSF.BF.B.3

Which transformation transforms the graph of
f(x) = x² to the graph of g(x) = (x + 4)²?

• a vertical translation 4 units up
• a vertical translation 4 units down
• a horizontal translation 4 units to the left
• a horizontal translation 4 units to the right

Tags

CCSS.HSF.BF.B.3

CCSS.HSG.CO.A.2

CCSS.HSG.CO.A.5

Which equation describes the transformation of shifting f(x)=x³ seven units up?

• x³+7
• x³-7
• (x-7)³
• (x+7)³

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 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

What transformation occurred to y = x⁶ to y = (x - 5)⁶ - 3?

• The graph translated right 5 units and down 3 units

• The graph translated right 3 units and down 5 units

• The graph translated left 5 units and down 3 units

• The graph translated left 3 units and up 5 units

g(x)=-f(x-3)+2

Describe the transformation to f(x) that results in g(x).

• f(x) has been reflected over the x-axis, shifted 3 units right and 2 units up.

• f(x) has been reflected over the y-axis, shifted 3 units left and 2 units up.

• f(x) has been reflected over the x-axis, shifted 3 units left and 2 units up.

• f(x) has been reflected over the y-axis, shifted 3 units right and 2 units up.

In the equation f(x)=1/2(x+9)²-1, what happens to the parabola?

• Reflect, horizontal compress by 1/2, left 9, down 1

• Vertical compress by 1/2, left 9, down 1

• Horizontal Compress by 1/2, right 9, down 1

• Vertical Stretch by 1/2, left 9, down 1

What is the new rule for g if you let g(x) = f(x) - 15 if

f(x) = .02x³ + 6x² + .2x + 125

write the parent function AND correct response on the answer sheet provided.

• .02x³ + .6x² + .2x + 110

• -.02x³ - .6x² - .2x - 125

• .02(-x)³ + .6(-x)² + .2(-x) + 125

• .02x³ - .6x² - .2x - 110

Tags

CCSS.HSF.BF.B.3