Function Transformations

Front

What is a vertical shift in function transformations?

Back

A vertical shift occurs when a function is moved up or down on the graph. For example, k(x) = f(x) + c shifts the graph up by c units, while k(x) = f(x) - c shifts it down by c units.

Front

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

Back

The transformation k(x) = f(x) - 9 represents a vertical shift down by 9 units.

Front

What is a horizontal shift in function transformations?

Back

A horizontal shift occurs when a function is moved left or right on the graph. For example, k(x) = f(x + c) shifts the graph left by c units, while k(x) = f(x - c) shifts it right by c units.

Front

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

Back

The transformation m(x) = f(x + 1) represents a horizontal shift left by 1 unit.

Front

What does the transformation f(x) = (x + 7)² represent?

Back

The transformation f(x) = (x + 7)² represents a horizontal shift left by 7 units compared to the parent function f(x) = x².

Front

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

Back

The transformation t(x) = f(x) - 1 represents a vertical shift down by 1 unit.

Front

What does the transformation w(x) = f(x - 7) represent?

Back

The transformation w(x) = f(x - 7) represents a horizontal shift right by 7 units.

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. For example, k(x) = af(x) where a > 1.

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. For example, k(x) = af(x) where 0 < a < 1.

Front

How does the transformation k(x) = 2f(x) affect the graph?

Back

The transformation k(x) = 2f(x) represents a vertical stretch by a factor of 2.