The Parent Function Graphs and Transformations

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 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

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.

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

• Shift down by 4

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

• Reflection over x-axis, steeper, up 5

• Reflection over y-axis, less steep, right 5

• Steeper, left 5

• reflection over x-axis, less steep, up 5

How did the equation shift from the parent function? y = f(x + 7)

• Up 7

• Down 7

• Left 7

• Right 7

How did the equation shift from the parent function?
y = 3f(x) - 2

• less steep and translate down 2

• Translate up 2

• Translate down 2

• steeper and translate down 2

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