Transformations of Parent Functions

Front

What is a transformation of a function?

Back

A transformation of a function refers to a change in the position, size, or shape of its graph. This can include translations, reflections, stretches, and compressions.

Tags

CCSS.HSF.BF.B.3

Front

What does it mean to shift a graph to the right?

Back

Shifting a graph to the right means adding a positive value to the input of the function. For example, in the function y = f(x - 4), the graph shifts right by 4 units.

Front

What is a vertical translation?

Back

A vertical translation moves the graph of a function up or down. For example, f(x) + 2 translates the graph up by 2 units.

Front

What is a horizontal translation?

Back

A horizontal translation moves the graph of a function left or right. For example, f(x + 3) translates the graph left by 3 units.

Front

What does a vertical stretch do to a graph?

Back

A vertical stretch increases the distance between points on the graph and the x-axis. For example, in y = 3f(x), the graph is stretched vertically by a factor of 3.

Front

What is a reflection in the x-axis?

Back

A reflection in the x-axis flips the graph over the x-axis. For example, y = -f(x) reflects the graph of f(x) across the x-axis.

Front

How does the equation y = f(x) - 5 transform the graph?

Back

The equation y = f(x) - 5 shifts the graph down by 5 units.

Front

What is the effect of replacing f(x) with f(x - 2)?

Back

Replacing f(x) with f(x - 2) shifts the graph to the right by 2 units.

Front

What does the equation y = 2 ext{sqrt}(x) represent?

Back

The equation y = 2 ext{sqrt}(x) represents a vertical stretch of the parent function y = ext{sqrt}(x) by a factor of 2.

Tags

CCSS.HSF-IF.C.7B

Front

What transformation occurs in the function g(x) = ext{sqrt}(x + 3)?

Back

The function g(x) = ext{sqrt}(x + 3) shifts the graph left by 3 units.

Tags

CCSS.HSF.BF.B.3