REVIEW - Transformation 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 reflect a function over the x-axis?

Back

Reflecting a function over the x-axis means that for every point (x, y) on the graph, the point (x, -y) will also be on the graph.

Front

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

Back

Reflecting a function over the y-axis means that for every point (x, y) on the graph, the point (-x, y) will also be on the graph.

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 shift a function up or down?

Back

Shifting a function up means adding a constant to the output values, while shifting down means subtracting a constant from the output values.

Front

What does the notation f(x) - 3 represent?

Back

The notation f(x) - 3 represents a vertical shift of the graph of f(x) down by 3 units.

Front

What does the notation -2f(x) represent?

Back

The notation -2f(x) represents a reflection of the graph of f(x) over the x-axis and a vertical stretch by a factor of 2.

Front

How do you describe the transformation of y = |x| to y = -2|x - 3| + 4?

Back

This transformation reflects the graph over the x-axis, stretches it vertically by a factor of 2, shifts it right by 3 units, and shifts it up by 4 units.

Front

What is the parent function of y = |x|?

Back

The parent function of y = |x| is the absolute value function, which outputs the non-negative value of x.