Review --- Transformations of Functions

Front

What is a transformation of a function?

Back

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

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, changing the sign of the output values.

Front

What is a vertical stretch?

Back

A vertical stretch occurs when the output values of a function are multiplied by a factor greater than 1, making the graph narrower.

Front

What is a vertical compression?

Back

A vertical compression occurs when the output values of a function are multiplied by a factor between 0 and 1, making the graph wider.

Front

How do you translate a function left or right?

Back

To translate a function left, you subtract from the input (x), and to translate it right, you add to the input (x).

Front

What is the parent function of a quadratic function?

Back

The parent function of a quadratic function is f(x) = x².

Front

How does the equation g(x) = -3x² transform the parent function?

Back

The equation g(x) = -3x² reflects the parent function over the x-axis and vertically stretches it by a factor of 3.

Front

What does it mean to shift a function down?

Back

Shifting a function down means subtracting a constant from the output values, moving the graph lower on the y-axis.

Front

What does it mean to shift a function up?

Back

Shifting a function up means adding a constant to the output values, moving the graph higher on the y-axis.

Front

How do you identify a function translated left 4 units?

Back

A function translated left 4 units can be identified by the form g(x) = f(x + 4).