Transformations of Functions

Given f(x) = (x-3)² + 5.  What transformations took place from the original function f(x)?

• Left 3 and up 5
• Right 3 and down 5
• Left 3 and down 5
• Right 3 and up 5

  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

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

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

Match the equation to its description.

• Right 2 and up 2

• Left 2 and up 2

• Right 2 and down 2

• Left 2 and down 2

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.

What is the rule for the transformation of g(x) in terms of f(x)?

• f(x)=g(x)-6
• g(x)=f(x)-6
• f(x)=g(x)+6
• g(x)=f(x)+6

Describe the transformation:

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

• Shift 3 units up

• Shift 3 units down

• Shift 3 units left

• Shift 3 units right

Describe the transformation:

 $h\left(x\right)=x^2+7$  

• Shift 7 units down

• Shift 7 units up

• Shift 7 units left

• Shift 7 units right

Describe the transformation:

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

• Shift 3 units up

• Shift 3 units down

• Shift 3 units left

• Shift 3 units right