Function Transformations

Front

What is a horizontal shift to the left in function transformations?

Back

A horizontal shift to the left occurs when the input of the function is increased by a constant. For example, m(x) = f(x + c) shifts the graph left by c units.

Front

What is a horizontal shift to the right in function transformations?

Back

A horizontal shift to the right occurs when the input of the function is decreased by a constant. For example, w(x) = f(x - c) shifts the graph right by c units.

Front

How does a vertical stretch affect a function?

Back

A vertical stretch occurs when the output of the function is multiplied by a factor greater than 1. For example, 2f(x) stretches the graph vertically by a factor of 2.

Front

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

Back

The transformation f(x) + k represents a vertical shift of the graph. If k is positive, the graph shifts up by k units; if k is negative, it shifts down by |k| units.

Front

What is the effect of the transformation f(x + c)?

Back

The transformation f(x + c) results in a horizontal shift of the graph to the left by c units.

Front

What is the effect of the transformation f(x - c)?

Back

The transformation f(x - c) results in a horizontal shift of the graph to the right by c units.

Front

What does a vertical compression by a factor of 1/k do to a function?

Back

A vertical compression by a factor of 1/k (where k > 1) reduces the height of the graph, making it flatter.

Front

How do you represent a vertical shift up by 3 units?

Back

A vertical shift up by 3 units is represented as f(x) + 3.

Front

How do you represent a vertical shift down by 2 units?

Back

A vertical shift down by 2 units is represented as f(x) - 2.

Front

What is the transformation for a vertical stretch by a factor of 3 and a left shift by 4 units?

Back

The transformation is represented as 3f(x + 4).