Transformations of Functions

Front

What is a transformation of a function?

Back

A transformation of a function is an operation that alters the graph of the function in some way, such as shifting, reflecting, stretching, or compressing.

Front

What does it mean to shift a graph left or right?

Back

Shifting a graph left or right involves moving the entire graph horizontally. A positive shift moves the graph to the right, while a negative shift moves it to the left.

Front

What does it mean to shift a graph up or down?

Back

Shifting a graph up or down involves moving the entire graph vertically. A positive shift moves the graph up, while a negative shift moves it down.

Front

What is a vertical stretch of a function?

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 of a function?

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 it mean to reflect a graph over the x-axis?

Back

Reflecting a graph over the x-axis means flipping the graph over the x-axis, which changes the sign of all output values.

Front

What does it mean to reflect a graph over the y-axis?

Back

Reflecting a graph over the y-axis means flipping the graph over the y-axis, which changes the sign of all input values.

Front

How does the function f(x) = x^2 transform to f(x) = (x - 3)^2?

Back

The graph of f(x) = x^2 is shifted right by 3 units.

Front

How does the function f(x) = x^2 transform to f(x) = -x^2?

Back

The graph of f(x) = x^2 is reflected over the x-axis.

Front

What is the effect of the transformation f(x) = 2√x?

Back

This transformation represents a vertical stretch of the parent function f(x) = √x by a factor of 2.