Function Transformations

If g(x) = -2f(x), what transformation is applied to the function f(x)?

• Reflection about the x-axis and vertical stretch by a factor of 2

• Reflection about the y-axis and horizontal stretch by a factor of 2

• Translation upwards by 2 units

• Rotation of 90 degrees counterclockwise

Explain how the function h(x) = 2f(3x) is related to the original function f(x).

• Multiplying the input by 2 and the output by 3

• Adding 3 to the input and multiplying the output by 2

• Scaling the input by 3 and the output by 2

• Dividing the input by 3 and the output by 2

What happens to the graph of the function y = f(x) when it is reflected over the x-axis?

• The graph of the function y = f(x) is reflected over the x-axis by changing the sign of the y-coordinates of all points.

• The graph is translated horizontally

• The graph is stretched vertically

• The graph is rotated 90 degrees counterclockwise

What is the result of shifting the function f(x) = x^2 three units to the right?

• f(x) = x^2 - 3

• f(x) = (x-3)^2

• f(x) = x^2 + 3

• f(x) = (x+3)^2

Describe the transformation involved in the function k(x) = f(x) + 4.

• Vertical shift of 4 units downwards

• Horizontal shift of 4 units to the left

• Reflection over the x-axis

• Vertical shift of 4 units upwards

If the function p(x) = f(x + 2) is shifted two units to the left, what is the resulting function?

• p(x) = f(x - 4)

• p(x) = f(x - 2)

• p(x) = f(x)

• p(x) = f(x + 4)

How does the function q(x) = -f(-x) differ from the original function f(x)?

• The function q(x) = -f(-x) differs from the original function f(x) by being reflected about both the x-axis and y-axis.

• The function q(x) = -f(-x) differs from the original function f(x) by being scaled.

• The function q(x) = -f(-x) differs from the original function f(x) by being shifted horizontally.

• The function q(x) = -f(-x) differs from the original function f(x) by being shifted vertically.

Explain the effect of multiplying the function r(x) = 0.5f(x) by 0.5.

• The effect of multiplying the function r(x) = 0.5f(x) by 0.5 is that the function values are halved compared to the original function values.

• The function values remain the same as the original function values.

• The function values are squared compared to the original function values.

• The function values are doubled compared to the original function values.