Shifts on a Linear Graph

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

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 4 units up from the graph f
• The graph of g is a horizontal translation of the graph of f, 4 units right
• The graph of g is a horizontal translation of the graph of f, 4 units left
• The graph of g is a vertical stretch of the graph of f, by a factor of 7

What type of translation occurs if g(x) = f(x) + k?

• Shifts up "k" units

• Shifts down "k" units

• Shifts left "k" units

• Shifts right "k" units

What type of translation occurs is g(x) = f(x - 4)

• Shift right by 4

• Shift left by 4

• Shift up by 4

• Shift down by 4

What type of translation occurs if g(x) = f(x + 7)

• Up 7

• Down 7

• Left 7

• Right 7

A student graphed f(x) = x and g(x) = f(x + 4). 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 4 units up to create the graph of g.

• The graph of f is shifted 4 units to the left to create the graph of g.

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 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

What translation occurs if g(x) = f(x-3)+5

• right 3, up 5

• left 3, up 5

• down 3, right 5

• down 3, left 5