Transformations of Linear Functions

Front

What is a vertical translation in the context of linear functions?

Back

A vertical translation occurs when a function is shifted up or down on the graph without changing its shape. For example, f(x) + d shifts the graph up by d units, while f(x) - d shifts it down by d units.

Front

What happens to the graph of f(x) when it is transformed to f(x) + 2?

Back

The graph of f(x) is vertically translated up by 2 units.

Front

What is a vertical stretch in linear functions?

Back

A vertical stretch occurs when the output values of a function are multiplied by a factor greater than 1, making the graph taller. For example, transforming f(x) to 2*f(x) stretches the graph vertically by a factor of 2.

Front

How does the equation y = f(x + 7) transform the graph of f?

Back

The graph of f is shifted left by 7 units.

Tags

CCSS.HSF.BF.B.3

Front

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

Back

This transformation results in a vertical stretch of the graph by a factor of 2.

Front

What does the equation y = f(x) - d represent?

Back

This equation represents a vertical translation down by d units.

Front

How does the transformation y = f(x) + d affect the graph?

Back

The graph of f is shifted up by d units.

Front

What is a reflection across the x-axis in linear functions?

Back

A reflection across the x-axis occurs when the output values of a function are multiplied by -1, flipping the graph over the x-axis.

Front

If f(x) is transformed to f(x - 3), what is the effect on the graph?

Back

The graph of f is shifted right by 3 units.

Front

What does a horizontal compression mean in the context of linear functions?

Back

A horizontal compression occurs when the input values of a function are multiplied by a factor greater than 1, making the graph narrower.