Transformations of Functions

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

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

Which equation below is a quadratic function translated left 4 units?

• y = x² + 4
• y = (x + 4)²
• y = (x - 4)²
• y = 4x²

Tags

CCSS.HSF.BF.B.3

Which equation below is a quadratic function translated up 5 units?

• y = x² + 5
• y = (x + 5)²
• y = 5x²
• y = -x² - 5

Tags

CCSS.HSF.BF.B.3

Describe the transformation

• left 2 up 5
• right 2 up 5
• left 2 down 5
• right 2 down 5

Tags

CCSS.HSF.BF.B.3

The function $g\left(x\right)$  is the function  $f\left(x\right)=2\left(x-1\right)^2+3$  shifted 3 units right and 2 units down.  Which of the following is the equation for  $g\left(x\right)?$  

•  $g\left(x\right)=2\left(x+2\right)^2+1$  

•  $g\left(x\right)=2\left(x-3\right)^2-2$  

•  $g\left(x\right)=2\left(x+3\right)^2-2$  

•  $g\left(x\right)=2\left(x-4\right)^2+1$  

  . 
The blue is f(x)=|x|, red must be

• g(x)=|x+2|
• g(x)=|x|+2
• g(x)=|x-2|
• g(x)=|x|-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

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

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

• The graph of y = f(x) was flipped vertically across the x axis. 
• The graph of y = f(x) was flipped horizontally across the y axis.
• The graph of y = f(x) was shifted down.
• The graph of y = f(x) was shifted up

Tags

CCSS.HSF.BF.B.3