Function Transformations

Front

What is a horizontal translation in function transformations?

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

A horizontal shift to the right by c units.

Front

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

Back

A horizontal shift to the left by c units.

Front

What is a vertical translation in function transformations?

Back

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

Front

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

Back

A vertical shift upward by k units.

Front

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

Back

A vertical shift downward by k units.

Front

What is a vertical stretch in function transformations?

Back

A vertical stretch occurs when the output of the function is multiplied by a factor greater than 1.

Front

What is a vertical compression in function transformations?

Back

A vertical compression occurs when the output of the function is multiplied by a factor between 0 and 1.

Front

How does the transformation y = af(x) affect the graph?

Back

If a > 1, the graph is vertically stretched; if 0 < a < 1, the graph is vertically compressed.

Front

What is the effect of a negative sign in front of a function, such as y = -f(x)?

Back

It reflects the graph across the x-axis.