10.10 Transformations

The graphs of linear functions f and g are shown on the grid. Which function is best represented by the graph of g?

The linear parent function, f(x) = x, is transformed to g(x) = f(x) - 6. Describe the transformation.

• g(x) is shifted up 6 units

• g(x) is shifted down 6 units

• g(x) is shifted left 6 units

• g(x) is shifted right 6 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 will occur if f(x) = x is replaced with 2f(x)?

• Vertical stretch by a factor of 2

• Vertical compression by a factor of 1/2

• Vertical translation up by 2 units.

• Horizontal compression by a factor of 1/2

A student graphed f(x) = x and g(x) = ⅓f(x). Which statement is true?

• The graph of f is steeper than the graph of g.

• The graph of f is less steep than the graph of g.

• The graph of f is shifted 2 units up to create the graph of g.

• The graph of f is shifted 2 units to the right to create the graph of g.

• Vertical stretch by a factor of 4

• Vertical compression by a factor of 1/4

• Vertical translation up by 1/4 units.

• Horizontal compression by a factor of 1/4

What is the linear parent function?

• y = x

• y = mx + b

• f(x) = 2x

• Not here

If the graph of the parent function f(x) = x is shifted 7 units
down, which of the following equations would the new graphed
line represent?

• f(x) = 7x
• f(x) = x - 7
• f(x) = x + 7
• f(x) = 7x - 7

Describe the transformation from the parent function: y = 3x + 5

• Steeper; Shift up 5 units

• Steeper; Shift down 5 units

• Flatter; Shift up 5 units

• Flatter; Shift down 5 units

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