Function Transformations

Front

What is a horizontal translation?

Back

A horizontal translation shifts the graph of a function left or right along the x-axis.

Front

What does the transformation f(x + c) represent?

Back

It represents a horizontal translation of the graph of f(x) to the left by c units if c is positive, and to the right if c is negative.

Front

What does the transformation f(x - c) represent?

Back

It represents a horizontal translation of the graph of f(x) to the right by c units.

Front

What is a vertical translation?

Back

A vertical translation shifts the graph of a function up or down along the y-axis.

Front

What does the transformation f(x) + c represent?

Back

It represents a vertical translation of the graph of f(x) up by c units if c is positive, and down if c is negative.

Front

What does the transformation f(x) - c represent?

Back

It represents a vertical translation of the graph of f(x) down by c units.

Front

What is a reflection in function transformations?

Back

A reflection flips the graph of a function over a specific axis, such as the x-axis or y-axis.

Front

What does the transformation -f(x) represent?

Back

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

Front

What does the transformation f(-x) represent?

Back

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

Front

What is a vertical stretch?

Back

A vertical stretch occurs when the output values of a function are multiplied by a factor greater than 1, making the graph taller.