Vertical Translations of Linear Functions

Front

What is a vertical translation of a function?

Back

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

Front

How does adding a positive number to a function affect its graph?

Back

Adding a positive number to a function translates the graph upward by that number of units.

Front

How does subtracting a positive number from a function affect its graph?

Back

Subtracting a positive number from a function translates the graph downward by that number of units.

Front

What is the parent function of linear functions?

Back

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

Front

If f(x) = x + 8, what type of translation is this?

Back

This represents a vertical translation up 8 units from the parent function.

Front

If f(x) = x - 3, what type of translation is this?

Back

This represents a vertical translation down 3 units from the parent function.

Front

What happens to the graph of f(x) = x + 4 compared to f(x) = x?

Back

The graph of f(x) = x + 4 is shifted up 4 units compared to the graph of f(x) = x.

Front

What happens to the graph of f(x) = x - 9 compared to f(x) = x?

Back

The graph of f(x) = x - 9 is shifted down 9 units compared to the graph of f(x) = x.

Front

If a function is translated vertically, what remains unchanged?

Back

The slope and shape of the graph remain unchanged during a vertical translation.

Front

What is the effect of a vertical translation on the x-intercept of a function?

Back

A vertical translation does not affect the x-intercept of the function.