Transformations of Functions

Front

What is a reflection over the y-axis?

Back

A transformation that flips a graph over the y-axis, changing the sign of the x-coordinates of all points on the graph.

Front

What does f(-x) represent in function transformations?

Back

It represents a reflection of the function f(x) over the y-axis.

Front

What is a reflection over the x-axis?

Back

A transformation that flips a graph over the x-axis, changing the sign of the y-coordinates of all points on the graph.

Front

What does -f(x) represent in function transformations?

Back

It represents a reflection of the function f(x) over the x-axis.

Front

What does f(x) + k represent?

Back

A vertical shift of the graph of f(x) upwards by k units if k is positive, and downwards if k is negative.

Front

What does f(x - h) represent?

Back

A horizontal shift of the graph of f(x) to the right by h units if h is positive, and to the left if h is negative.

Front

What is the effect of adding a constant to a function?

Back

It shifts the graph vertically without changing its shape.

Front

What is the effect of subtracting a constant from a function?

Back

It shifts the graph vertically downwards without changing its shape.

Front

What does (x - h)^2 represent in transformations?

Back

A horizontal shift of the graph of f(x) to the right by h units.

Front

What does (x + h)^2 represent in transformations?

Back

A horizontal shift of the graph of f(x) to the left by h units.