4B Transformations of Functions

Describe the transformation: (click on two answers)

 $h\left(x\right)=\left(x-1\right)^2+5$  

• Shift 1 unit left

• Shift 1 unit right

• Shift 5 units up

• Shift 5 units down

Describe the transformation: (click on two answers)

 $f\left(x\right)=-x^2-7$  

• Reflection over the x-axis

• Reflection over the y-axis

• Shift 7 units up

• Shift 7 units down

 If the blue graph is the parent function, what is the equation of the red (transformed) function?

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

The graph shows the function f(x)=x² in blue and another function g(x) in red. Which could be the equation for g(x)?

• A. g(x)=3x²

• B. g(x)=-3x²

• C. g(x) = x² - 3

• D. g(x) = (x-3)²

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

Which equation describes the transformation of shifting f(x)=x³ four units down?

• x³+ 4
• x³- 4
• (x - 4)³
• (x + 4)³

Which equation describes the transformation of shifting f(x)=x³ three units left?

• x³ + 3
• x³ - 3
• (x + 3)³
• (x - 3)³

• f(x) = −(x−2)³−1
• f(x) = −(x+2)³−1
• f(x) = −(x−2)³ + 1
• f(x) = −(x+2)³ + 1

What is the equation of this graph?

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

Identify the transformation from the graph of f(x)=x² to the graph g(x)= -(x+5)²

• shifted up five units

  reflection in x-axis

• shifted down five units

  reflection in x-axis

• shifted left 5 units

  reflection x-axis

• shifted right 5 units

  reflection x-axis