Transformations of Functions and Graphs

Front

What is a transformation of a function?

Back

A transformation of a function refers to the changes made to the graph of a function, which can include translations, reflections, stretches, and compressions.

Front

What is a vertical translation?

Back

A vertical translation shifts the graph of a function up or down. For example, if f(x) = x^2, then g(x) = x^2 + 5 shifts the graph up by 5 units.

Front

What is a horizontal translation?

Back

A horizontal translation shifts the graph of a function left or right. For example, if f(x) = x^2, then g(x) = (x - 5)^2 shifts the graph right by 5 units.

Front

What is a reflection in the x-axis?

Back

A reflection in the x-axis flips the graph of a function over the x-axis. For example, if f(x) = x^2, then g(x) = -x^2 reflects the graph over the x-axis.

Front

What is a reflection in the y-axis?

Back

A reflection in the y-axis flips the graph of a function over the y-axis. For example, if f(x) = x^2, then g(x) = (-x)^2 reflects the graph over the y-axis.

Front

What is a vertical stretch?

Back

A vertical stretch occurs when the graph of a function is stretched away from the x-axis. For example, if f(x) = x^2, then g(x) = 2x^2 stretches the graph vertically by a factor of 2.

Front

What is a vertical compression?

Back

A vertical compression occurs when the graph of a function is compressed towards the x-axis. For example, if f(x) = x^2, then g(x) = 0.5x^2 compresses the graph vertically by a factor of 0.5.

Front

What is the domain of a function?

Back

The domain of a function is the set of all possible input values (x-values) for which the function is defined.

Front

What is the range of a function?

Back

The range of a function is the set of all possible output values (y-values) that the function can produce.

Front

How do you find the x-intercepts of a function?

Back

To find the x-intercepts of a function, set the function equal to zero and solve for x. The solutions are the x-intercepts.