Vertical Shifts 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

It shifts the graph upward by that number.

Front

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

Back

It shifts the graph downward by that number.

Front

What is the general form of a vertically shifted function?

Back

g(x) = f(x) + k, where k is the amount of vertical shift.

Front

If g(x) = f(x) - 125, what transformation does this represent?

Back

This represents a downward shift of 125 units.

Front

If g(x) = f(x) + 46, what transformation does this represent?

Back

This represents an upward shift of 46 units.

Front

What does the equation g(x) = f(x) + 5 represent?

Back

It represents an upward shift of 5 units.

Front

What does the equation g(x) = f(x) - 97 represent?

Back

It represents a downward shift of 97 units.

Front

What happens to the graph of f(x) when you replace it with g(x) = f(x + c)?

Back

This represents a horizontal shift, not a vertical shift.

Front

What is the effect of the transformation g(x) = f(x) + k when k is negative?

Back

It shifts the graph downward by the absolute value of k.