Transformations of Functions and Graphs

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.

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.

If the blue graph is
f(x) = x² 
then the red must be...

• g(x) = x² - 5

• g(x) = x² + 5

• g(x) = (x - 5)²

• g(x) = (x + 5)²

Which transformation on f(x) = x is g(x) = -f(x)

• Reflection across the y-axis

• The slope will be less steep

• The graph will be wider

• Reflection across the x-axis.

Match the equation to its description.

• Reflected over x, right 2 and up 1

• Reflected over x, left 2 and up 1

• Reflected over x, right 2 and down 1

• Reflected over x, left 2 and down 1

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

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.

Identify the coordinates of the point (3 , -2), translated 5 units left and 6 units up.

• (2,-4)

• (-2,4)

• (8,4)

• (-2,-8)

How did we transform from f(x) =x² 
to
g(x) = -3x²

• reflection in x-axis and vertical shift down

• reflection x-axis and vertical stretch

• horizontal stretch

• reflection x-axis and vertical compression