Transformations of Functions

What transformations occur in the function f(x) = (1/2)f(x) + 4?

• Vertical stretch by 2, vertical shift up 4 units.

• Vertical compression by 1/2, vertical shift up 4 units.

• Vertical compression by 1/2, horizontal shift right 4 units.

• Vertical stretch by 2, horizontal shift left 4 units.

Describe the transformations in the function f(x) = 2f(x - 3).

• Vertical stretch by 2, horizontal shift right 3 units.

• Vertical compression by 1/2, horizontal shift left 3 units.

• Vertical stretch by 2, horizontal shift left 3 units.

• Vertical compression by 1/2, horizontal shift right 3 units.

What transformations are represented by the function f(x) = -5f(x + 1)?

• Vertical stretch by 5, reflection over x-axis, horizontal shift right 1 unit.

• Vertical compression by 1/5, reflection over x-axis, horizontal shift left 1 unit.

• Vertical stretch by 5, reflection over x-axis, horizontal shift left 1 unit.

• Vertical compression by 1/5, reflection over y-axis, horizontal shift right 1 unit.

What transformations are applied to the parent function f(x) to obtain f(x) = f(-2x) - 3?

• Horizontal compression by 1/2, reflection over y-axis, vertical shift down 3 units

• Horizontal stretch by 2, reflection over y-axis, vertical shift down 3 units

• Vertical compression by 1/2, reflection over x-axis, vertical shift down 3 units

• Horizontal compression by 1/2, reflection over x-axis, vertical shift up 3 units

Describe the transformations applied to the parent function f(x) to obtain f(x) = 1/2(x-3)^3 + 4.

• Vertical compression by 1/2, horizontal shift left 3 units, vertical shift up 4 units

• Vertical compression by 1/2, horizontal shift right 3 units, vertical shift up 4 units

• Vertical stretch by 2, horizontal shift right 3 units, vertical shift down 4 units

• Horizontal compression by 1/2, horizontal shift right 3 units, vertical shift up 4 units

What transformations are applied to the parent function f(x) to obtain f(x) = 2(x+1)^3?

• Vertical stretch by 2, horizontal shift left 1 unit

• Vertical compression by 1/2, horizontal shift right 1 unit

• Vertical stretch by 2, horizontal shift right 1 unit

• Vertical compression by 1/2, horizontal shift left 1 unit

Describe the transformations applied to the parent function f(x) to obtain f(x) = -3x^3 - 2.

• Reflection over x-axis, vertical stretch by 3, vertical shift down 2 units

• Reflection over y-axis, vertical stretch by 3, vertical shift down 2 units

• Reflection over x-axis, vertical compression by 1/3, vertical shift up 2 units

• Reflection over y-axis, vertical compression by 1/3, vertical shift up 2 units