STATION 3: Transformations of Linear Functions

Front

What is a vertical translation of a function?

Back

A vertical translation moves the graph of a function up or down without changing its shape.

Front

What happens to the function f(x) when it is replaced with f(x) + 2?

Back

The graph of the function shifts vertically up by 2 units.

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 transformation occurs when f(x) is replaced with 2f(x)?

Back

The graph undergoes a vertical stretch by a factor of 2.

Front

How can you identify a linear function?

Back

A function is linear if it can be represented by a straight line on a graph, typically in the form y = mx + b.

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.

Front

What is a horizontal stretch of a function?

Back

A horizontal stretch occurs when the input values of a function are multiplied by a factor less than 1, making the graph wider.

Front

What transformation is represented by the equation f(-1/2x) - 4?

Back

This equation represents a horizontal stretch by a factor of 2, a reflection over the x-axis, and a vertical shift down by 4.

Front

What does the equation y = f(x - 4) indicate about the transformation?

Back

This equation indicates a horizontal shift of the graph to the right by 4 units.

Front

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

Back

This transformation reflects the graph of the function across the x-axis.