Function Transformations

Front

What is a function transformation?

Back

A function transformation refers to the changes made to the graph of a function, which can include shifts, stretches, compressions, and reflections.

Front

What does the transformation t(x) = f(x) - 1 represent?

Back

The graph of the function f(x) is shifted down by 1 unit.

Front

What does the transformation m(x) = f(x + 1) represent?

Back

The graph of the function f(x) is shifted left by 1 unit.

Front

Given f(x) = (x-3)² + 5, what transformations occurred?

Back

The graph of the function is shifted right by 3 units and up by 5 units.

Front

What does the transformation k(x) = f(x) - 9 represent?

Back

The graph of the function f(x) is shifted down by 9 units.

Front

What is the parent function of a linear function?

Back

The parent function of a linear function is f(x) = x.

Front

What is a vertical stretch in function transformations?

Back

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

Front

What is a vertical compression in function transformations?

Back

A vertical compression occurs when the output values of a function are multiplied by a factor between 0 and 1, making the graph shorter.

Front

What does a horizontal shift to the right mean in function transformations?

Back

A horizontal shift to the right means the graph of the function is moved to the right along the x-axis.

Front

What does a horizontal shift to the left mean in function transformations?

Back

A horizontal shift to the left means the graph of the function is moved to the left along the x-axis.