Alg2 Unit 6 Review - 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

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)

  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

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

Identify the transformations.

• horizontal shift to the left 2 and vertical stretch by a factor of 3

• horizontal shift to the right 2 and vertical stretch by a factor of 3

• horizontal shift to the right 2 and vertical compression by a factor of 3

• horizontal shift to the left 2 and vertical compression by a factor of 3

The original function has equation f(x). State the transformations given the new function f(x) = ⅔(x - 7)²

• Vertical compression of ⅔

  Right 7

• Horizontal compression of ⅔

  Left 7

• Left ⅔

  Vertical stretch of 7

• Right ⅔

  Horizontal stretch of 7

The vertex of the quadratic function f(x) in the picture is (-4, 5). If g(x) = f(x + 2) , what is the vertex of g(x)?

• (-2, 5)
• (-6, 5)
• (-4, 3)
• (-4, 7)

 f(x) is transformed so that it maps onto g(x). Which equation would correctly represent g(x)

• g(x)=2f(x)
• g(x)=0.5f(x)
• g(x)=f(x) + 2
• g(x)=f(x + 2)

Describe the transformations that maps

y = g(x) to y = - g(x + 6) - 10

• Shifted left 6 units

  Reflect over y-axis

  Shifted down 10 units

• Shifted left 6 units

  Reflect over x-axis

  Shifted up 10 units

• Shifted right 6 units

  Reflect over y-axis

  Shifted up 10 units

• Shifted left 6 units

  Reflect over x-axis

  Shifted down 10 units

. 
If the blue is f(x)=x^2, then the red must be

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