Transformations of Functions Review

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)

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

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)
Describe the transformation to f(x) that results in g(x).

• f(x) has been reflected over the x-axis.
• f(x) has been reflected over the y-axis.

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

• a translation shifting f(x) 4 units up
• a translation shifting f(x) 4 units down
• a translation shifting f(x) 4 units to the left
• a translation shifting f(x) 4 units to the right

Which transformation will occur if f(x) = x² is replaced with 2⋅f(x)?

• Vertical Compression by a factor of 2
• Vertical Stretch by a factor of 2
• Vertical translation up by 2 units.
• Reflection across the x-axis.

A student graphed f(x) = x and g(x) = f(x) - 12. Which statement is true?

• The graph of f is shifted 12 units to the right to create the graph of g.

• The graph of f is shifted 12 units down to create the graph of g.

• The graph of f is shifted 12 units up to create the graph of g.

• The graph of f is shifted 12 units to the left to create the graph of g.

How did the equation shift from the parent function?

y = f(x) + c

• Shifted up "c" units

• Shifted down "c" units

• Stretches vertically

• Shifted right "c" units

Compare the function y = 5x² to the parent function y = x²

• Wider
• Narrower