Translations of Linear Functions

Front

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

Back

A vertical translation is a shift of a function up or down on the graph, determined by adding or subtracting a constant from the function's output.

Front

How does adding a positive constant affect the graph of a linear function?

Back

Adding a positive constant results in a vertical translation upwards by that constant's value.

Front

How does subtracting a constant affect the graph of a linear function?

Back

Subtracting a constant results in a vertical translation downwards by that constant's value.

Front

What is the parent function of linear functions?

Back

The parent function of linear functions is f(x) = x, which represents a straight line through the origin with a slope of 1.

Front

If a function is translated vertically up by 8 units, what is the new function if the original function is f(x)?

Back

The new function is f(x) + 8.

Front

If a function is translated vertically down by 9 units, what is the new function if the original function is f(x)?

Back

The new function is f(x) - 9.

Front

What does it mean if a function is described as having a vertical translation of 4 units up?

Back

It means that every point on the graph of the function is moved 4 units higher on the y-axis.

Front

What does it mean if a function is described as having a vertical translation of 3 units down?

Back

It means that every point on the graph of the function is moved 3 units lower on the y-axis.

Front

How can you determine the direction of a vertical translation from a function's equation?

Back

If the equation has a positive constant added, it translates up; if it has a negative constant subtracted, it translates down.

Front

What is the effect of a vertical translation on the slope of a linear function?

Back

A vertical translation does not affect the slope of the linear function; it only shifts the graph up or down.