Transformations Review

Match each equation below with the verbal description of its transformation from the linear parent function, f(x) = x.

• k(x) = (4x + 3) – 5

• The graph is a vertical stretch by a factor of 4, a translation to the right 3 units, and a translation up 5 units.

• g(x) = 4(x – 3) + 5

• The graph is a reflection over the x-axis, a vertical expansion by a factor of 4, a translation to the right 3 units, and a translation down 5 units.

• h(x) = (4x – 3) + 5

• The graph is a horizontal compression by a factor of one-fourth, a translation to the left of 3/4 units, and a translation down 5 units.

• j(x) = –4(x – 3) – 5

• The graph is a horizontal compression by a factor of one-fourth, a translation to the right of 3/4 units, and a translation up 5 units.

Describe the transformations of the linear parent function, f(x) = x, that will result in the graph of the linear function

h(x) = 3(x + 2).

• vertical stretch by a factor of two and translation three units to the left

• vertical stretch by a factor of three and translation two units to the left

• vertical stretch by a factor of two and translation three units to the right

• vertical compression by a factor of one-third and translation two units to the right

Identify which of the functions is the result of the following transformations to the graph of the quadratic parent function f(x) = x².

• k(x) = 3(x - 2)²

• a translation of 3 units to the left and 2 units down

• h(x) = 3x² + 2

• horizontal stretch by a factor of 1/3 and a translation of 2/3 units to the left

• g(x) = (x + 3)² – 2

• vertical stretch by a factor of 3 and a translation of 2 units to the right

• j(x) = (1/3x + 2/3)²

• vertical stretch by a factor of 3 and a translation of 2 units up

Describe the transformations of the cubic parent function, f(x) = x³ that will result in the function h(x) = –2(x + 1)³ – 9.

• vertical stretch by a factor of 1/2 , reflection over the y-axis, and translation 1 unit left and 9 units up

• vertical stretch by a factor of 2, reflection over the x-axis, and translation 1 unit left and 9 units up

• vertical stretch by a factor of 2, reflection over the x-axis, and translation 1 unit left and 9 units down

• vertical stretch by a factor of 9, reflection over the y-axis, and translation 1 unit right and 2 units down

Identify the transformations to the step function: 

• x-axis reflection; stretch of 2; right 2; down 2
• x-axis reflection; stretch of 2; left 2; down 2
• x-axis reflection; shrink of 2; left 2; up 2
• shrink of -2; right 2; down 2

Identify the transformations: 

• x-axis reflection; shrink of 0.2; right 1.5; up 1
• shrink of -0.2; right 1.5; up 1
• shrink of -0.2; left 1.5; down 1
• x-axis reflection; shrink of -0.2; right 1.5; up 1

Describe the transformation that occurred

p(x) = f(x + 3)

• Right 3 units

• Vertical Stretch

• Up 3 units

• Left 3 units

Describe the transformation that occurred.

h(x) = f(x) + 2

• up 2 units

• left 2 units

• Vertical Strech

• right 2 units

Find the equation of the parabola that has...

moved 3 units to the left

moved 5 units up

Find the equation of the parabola that has...

been reflected

stretched by 5