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)

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

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 - 15). Which statement is true?

• The graph of f is shifted 15 units to the right to create the graph of g.

• The graph of f is shifted 15 units down to create the graph of g.

• The graph of f is shifted 15 units up to create the graph of g.

• The graph of f is shifted 15 units to the left to create the graph of g.

• Shift 1 unit left

• Shift 1 unit right

• Shift 5 units up

• Shift 5 units down

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

In the equation f(x)=5(x+3)²-10 what does the 5 do?

• Vertical stretch by 5
• Horizontal compress by 5
• Reflect
• Move up 5

What is the vertical shift of this equation?
f(x) = -(x + 3)² - 5

• left 5
• right 5
• up 5
• down 5