Transforming Polynomial Functions

The graph of y = g(x) shown is the result of shifting the graph of f(x) 3 units to the right and 2 units up. If the equation of g is g(x) = x² - 2x +2, what is the equation of f(x)?

• f(x) = x² + 4x + 3

• f(x) = x² + 4x + 15

• f(x) = x² + 6x + 19

• f(x) = x² - 8x + 15

• f(x) = x² - 8x + 19

the graph of y = f(x) is shown. Which of the following is the graph of y = f ( - x) - 2?

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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.

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)

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

State the transformations given the new function f(x) = ⅔(x - 7)² 

• Vertical Shrink of ⅔
  Right 7

• Horizontal Shrink 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)

When the number multiplied in front is greater than 1, the graph becomes...

• backwards

• upside down

• more steep

• less steep

Name the transformation(s) of this function compared to it's parent function:

y=3\left(2\right)^x-3

• more steep, up 3

• more steep, down 3

• less steep, left 3

• less steep, right 3

Name the transformation(s) of this function compared to it's parent function:

y=-\frac{1}{2}\left(2\right)^x

• down 1/2

• right 1/2

• flips, less steep

• flips, more steep