Transformations Linear Functions

Which of the following g(x) equations is vertically stretched and shifted down from f(x) = x?

• g(x) = 2 f(x) + 6

• g(x) = 1/2 f(x) + 6

• g(x) = 2 f(x) - 6

• g(x) = 1/2 f(x) - 6

Describe the transformation in g(x) as it relates to the graph of the parent function.

g(x) = x + 3

• vertical translation down 3 units

• vertical translation up 3 units

• horizontal translation right 3 units

• horizontal translation left 3 units

Select the correct equation for the graph.

• y = 3x + 2

• y = -3x + 2

• y = ⅓x + 2

• y = -⅓x + 2

Describe the transformation in g(x) as it relates to the graph of the parent function.

g(x) = (x - 5)

• vertical translation down 5 units

• vertical translation up 5 units

• horizontal translation right 5 units

• horizontal translation left 5 units

Use the graphs of f and g to describe the transformation from the graph of f to the graph of g.

• The graph of g is a vertical translation 2 units up of the graph of f

• The graph of f is a horizontal translation two units left of g

• The graph of g is a vertical stretch by a factor of 2 of the graph of f

• The graph of g is a reflection of the graph of f

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.

How did the equation f(x) = x change if

g(x) = 1/2f(x) + 11

• Vertical stretch and shift up 11

• Horizontal shrink and shift down 11

• Vertical shrink and shift up 11

• Horizontal stretch and shift down 11

If the graph of the parent function f(x) = x is shifted 7 units up and is horizontally compressed by a factor of 3, what is the function?

• g(x) = f(7x) + 3

• g(x) = 3f(x) - 7

• g(x) = f(3x) + 7

• g(x) = 7x - 3

Which equation transforms f(x) = x to a horizontal stretch by a factor of 2, a reflection over the x axis, and a shift down 4?

• f(-2x - 4)

• f(-1/2x) - 4

• -f(2x) - 4

• -f(1/2x) - 4

Describe how the graph g(x) compares with f(x).

f(x) = 5x + 2

g(x) = 5(x + 7) + 2

• Up 7

• Down 7

• Left 7

• Right 7