Transformations of Functions

If the blue is  $f\left(x\right)=x^2$   the red must be ______.

•  $g(x)=f(x+2)$  

•  $g(x)=f(x-2)$  

•  $g(x)=f(x)+2$  

•  $g(x)=f(x)-2$  

What transformations to the parent function  $f\left(x\right)=\sqrt{x}$  result in  $g\left(x\right)=2\sqrt{x+4}-5$  ?

• Stretch by 2, shift left 4, shift up 5

• Stretch by 2, shift right 4, shift up 5

• Stretch by 2, shift left 4, shift down 5

• Stretch by 2, shift right 4, shift down 5

What transformations to the parent function  $f\left(x\right)=\left|x\right|$  result in  $g\left(x\right)=\frac{1}{2}\left|x\right|+3$  

• Compress by  $\frac{1}{2}$  , shift up 3

• Compress by  $\frac{1}{2}$  , shift down 3

• Stretch by  $\frac{1}{2}$  , shift right 3

• Stretch by  $\frac{1}{2}$  , shift left 3

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

Tags

CCSS.HSA.REI.D.11

CCSS.HSF.BF.B.3

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

• g(x)=√(-x)
• g(x)=√(x-1)
• g(x)=√x-1
• g(x)=-√x

Tags

CCSS.HSA.REI.D.10

CCSS.HSA.REI.D.11

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

g(x)=f(x-1)-5
Describe the transformation to f(x) that results in g(x).

• f(x) has been translated to the left one and down five.
• f(x) has been translated to the right one and down five.
• f(x) has been translated to the left one and up five.
• f(x) has been translated to the right one and up five.

Tags

CCSS.HSF.BF.B.3

CCSS.HSG.CO.A.2

  The blue function is the parent 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

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

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

• a reflection across the line x = -4
• a reflection across the line y = -4
• a translation shifting f(x) 4 units to the left
• a translation shifting f(x) 4 units to the right

Tags

CCSS.HSF.BF.B.3

CCSS.HSG.CO.A.2

CCSS.HSG.CO.A.4

If the yellow curve has equation f(x)=x²,

• Then the blue curve is f(x) = x² - c
• Then the blue curve is f(x) = (x+c)²
• Then the blue curve is f(x) = (x-c)²
• Then the blue curve is f(x) = x² + c

Tags

CCSS.HSF.BF.B.3

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

What are the transformations to the graph compared to the parent function y=√(x)?

• Shifted right 2, shifted up 3, and reflected over the y-axis
• Shifted left 2, shifted up 3, and reflected over the y-axis
• Shifted left 2, shifted up 3, and reflected over the x-axis
• Shifted right 2, shifted up 3, and reflected over the x-axis

Tags

CCSS.HSF.BF.B.3

CCSS.HSF.IF.C.7

CCSS.HSG.CO.A.2