Transformations of Linear Functions

Front

What is the parent function of linear functions?

Back

f(x) = x

Front

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

Back

Vertical translation up by 2 units.

Front

How does the function g(x) = -2/3f(x) - 2 transform the parent function?

Back

It shifts down 2 units, has a vertical compression of 2/3, and is reflected over the x-axis.

Front

What does the equation y = 3f(x) - 2 represent in terms of transformations?

Back

It represents a vertical stretch by 3 and a translation down 2 units.

Front

What transformation occurs when g(x) = 2f(x) is created from f(x) = x?

Back

Vertical stretch by a factor of 2.

Front

What is a vertical translation in the context of function transformations?

Back

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

Front

What is a vertical stretch in function transformations?

Back

A vertical stretch increases the distance between points on the graph and the x-axis, making the graph taller.

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 is the effect of a vertical compression on a function?

Back

A vertical compression decreases the distance between points on the graph and the x-axis, making the graph flatter.

Front

How can you identify a vertical translation from a function's equation?

Back

A vertical translation can be identified by a constant added or subtracted from the function, such as f(x) + k.