Transformations of Functions and Quadratic Formula

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)

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.

How did the equation shift from the parent function? y=(x)+2

• Shift up 2
• Shift down 2
• steeper
• flipped

The graph on the side represents f(x).

Which graph best represents f(-x).

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The graph to the side shows the function f(x).

Which graph represents the function f(x + 2)?

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The graph of y = f(x) is shown to the side.

What is the graph of y = f(x + 1) - 2?

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