Vertical 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 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 a linear function?

Back

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

Front

If f(x) = x + 4, what type of translation does this represent?

Back

This represents a vertical translation up 4 units from the parent function.

Front

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

Back

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

Front

What happens to the graph of f(x) = x + 8 compared to f(x) = x?

Back

The graph of f(x) = x + 8 is shifted up 8 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 down 4 units, what is the new function if the original is f(x) = x?

Back

The new function is f(x) = x - 4.

Front

If a function is translated vertically up 5 units, what is the new function if the original is f(x) = 2x?

Back

The new function is f(x) = 2x + 5.