Translating Linear Functions

What is the effect of adding a positive number to the input of a function?

• It results in a horizontal translation to the left.

• It results in a vertical translation upwards.

• It results in a horizontal translation to the right.

• It results in a vertical translation downwards.

What is a vertical translation in the context of graph transformations?

• A vertical translation shifts the graph up or down without changing its shape.

• A vertical translation rotates the graph around a point.

• A vertical translation stretches the graph horizontally.

• A vertical translation reflects the graph across the x-axis.

What does the equation m(x) = f(x + 2) represent?

• A horizontal translation of the graph of f left by 2 units.

• A vertical translation of the graph of f up by 2 units.

• A reflection of the graph of f across the x-axis.

• A horizontal translation of the graph of f right by 2 units.

What does the equation g(x) = f(x - 4) represent?

• A horizontal translation of the graph of f right by 4 units.

• A vertical translation of the graph of f up by 4 units.

• A reflection of the graph of f across the x-axis.

• A horizontal compression of the graph of f by a factor of 4.

If m(x) = f(x + 3), what type of transformation is this?

• A horizontal translation left by 3 units.

• A vertical translation up by 3 units.

• A horizontal translation right by 3 units.

• A vertical translation down by 3 units.

What does the equation k(x) = f(x) - 3 represent?

• A vertical translation of the graph of f down by 3 units.

• A horizontal translation of the graph of f to the left by 3 units.

• A vertical stretch of the graph of f by a factor of 3.

• A reflection of the graph of f across the x-axis.

What is the effect of subtracting a positive number from the output of a function?

• It results in a vertical translation up.

• It results in a vertical translation down.

• It results in a horizontal translation left.

• It results in a horizontal translation right.

What is the general form of a horizontal translation?

• g(x) = f(x + h), where h is a constant.

• g(x) = f(x - h), where h is a constant.

• g(x) = f(h - x), where h is a constant.

• g(x) = f(x), where h is a constant.

If f(x) = -x + 4, what is the translated function for g(x) = f(x + 3)?

• g(x) = -x + 1.

• g(x) = -x + 7.

• g(x) = -x + 4.

• g(x) = -x + 3.

If k(x) = f(x) + 2, what type of transformation is this?

• A vertical translation down by 2 units.

• A vertical translation up by 2 units.

• A horizontal translation left by 2 units.

• A horizontal translation right by 2 units.