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 translations, reflections, stretches, and compressions.

Front

What is a parent function?

Back

A parent function is the simplest form of a function type, from which other functions in the same family are derived.

Front

What does a vertical stretch do to a function?

Back

A vertical stretch increases the distance between points on the graph and the x-axis, making the graph taller.

Front

What does a vertical compression do to a function?

Back

A vertical compression decreases the distance between points on the graph and the x-axis, making the graph shorter.

Front

What is the effect of adding a constant to a function, f(x) + k?

Back

Adding a constant k to a function translates the graph vertically by k units. If k is positive, the graph moves up; if k is negative, it moves down.

Front

What is the effect of subtracting a constant from the input, f(x - h)?

Back

Subtracting a constant h from the input translates the graph horizontally to the right by h units.

Front

What is the effect of adding a constant to the input, f(x + h)?

Back

Adding a constant h to the input translates the graph horizontally to the left by h units.

Front

What does a reflection over the x-axis do to a function?

Back

A reflection over the x-axis flips the graph of the function upside down.

Front

What does a reflection over the y-axis do to a function?

Back

A reflection over the y-axis flips the graph of the function horizontally.

Front

How do you represent a vertical stretch by a factor of a?

Back

A vertical stretch by a factor of a is represented as f(x) = a * f(x), where a > 1.