Algebra: Vertical Shifts of Functions

Front

What is a vertical shift in a function?

Back

A vertical shift is a transformation that moves a graph 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 shifts the graph upward by that number.

Front

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

Back

Subtracting a positive number shifts the graph downward by that number.

Front

What is the effect of the expression f(x) + 4 on the graph of f(x)?

Back

It shifts the graph of f(x) upward by 4 units.

Front

What is the effect of the expression g(x) - 4 on the graph of g(x)?

Back

It shifts the graph of g(x) downward by 4 units.

Front

If f(x) is shifted up by 5 units, what expression represents this transformation?

Back

f(x) + 5.

Front

If g(x) is shifted down by 6 units, what expression represents this transformation?

Back

g(x) - 6.

Front

What does the expression f(x) + k represent, where k is a positive number?

Back

It represents a vertical shift of the graph of f(x) upward by k units.

Front

What does the expression f(x) - k represent, where k is a positive number?

Back

It represents a vertical shift of the graph of f(x) downward by k units.

Front

What is the general rule for vertical shifts of functions?

Back

Adding a number shifts the graph up, while subtracting a number shifts it down.