Transformations of Linear Functions

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

Which transformation will occur if f(x) = x is replaced with 2⋅f(x)?

• Vertical stretch
• Vertical compression
• Vertical translation up by 2 units.
  Horizontal stretch
• Horizontal compression

Which transformation will occur if f(x) = x is replaced with f(x) + 2?

• Translation left 2 units
• Translation right 2 units
• Vertical translation up by 2 units.
• Reflection across the x-axis.

Which transformation will occur if f(x) = x is replaced with -f(x)?

• Reflection across the y-axis
• Narrower
• Vertical translation up by 2 units.
• Reflection across the x-axis.

How did the equation shift from the parent function?
y = f(x) + d

• Shifted up "d" units
• Shifted down "d" units
• Stretches vertically
• Stretches horizontally

How did the equation shift from the parent function?
y = f(x - 4)

• Shift right by 4
• Shift left by 4
• Horizontal Stretch by 4
• Vertical Stretch by 4

How did the equation shift from the parent function?
y=(1/2)x+11

• Vertical stretch and shift up 11
• Horizontal compress and shift down 11
• Vertical compress 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?

• f(x) = 7x + 3
• f(x) = 3x - 7
• f(x) = 3x + 7
• f(x) = 7x - 3

How did the equation shift from the parent function?
y = -3f(x) + 5

• Reflection over x-axis, steeper, up 5
• Reflection over y-axis
• Steeper, down 5
• Moved right