Function Transformations

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 'squish' towards the x-axis.

Front

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

Back

This transformation shifts the graph of f(x) vertically by k units. If k is positive, the graph moves up; if k is negative, it moves down.

Front

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

Back

This transformation shifts the graph of f(x) horizontally. If c is positive, the graph moves left; if c is negative, it moves right.

Front

Describe the transformation that occurs in t(x) = f(x) - 1.

Back

This transformation shifts the graph of f(x) down by 1 unit.

Front

What is the effect of multiplying a function by a factor greater than 1?

Back

Multiplying a function by a factor greater than 1 results in a vertical stretch, making the graph taller.

Front

What does the transformation g(x) = f(x - 4) represent?

Back

This transformation shifts the graph of f(x) to the right by 4 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 'stretch' away from the x-axis.

Front

How does the transformation h(x) = 1/5f(x) affect the graph of f(x)?

Back

This transformation compresses the graph of f(x) vertically by a factor of 1/5.

Front

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

Back

A negative sign reflects the graph of the function across the x-axis.

Front

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

Back

This transformation reflects the graph of f(x) across the y-axis.