Vertical and Horizontal Shifts

Front

What is a vertical shift in a graph?

Back

A vertical shift occurs when a graph is moved up or down without changing its shape. For example, y = f(x) + k shifts the graph of f(x) up by k units if k > 0 and down by k units if k < 0.

Front

What is a horizontal shift in a graph?

Back

A horizontal shift occurs when a graph is moved left or right. For example, y = f(x - h) shifts the graph of f(x) right by h units if h > 0 and left by h units if h < 0.

Front

How does the equation y = (x + 2)^2 transform the graph of y = x^2?

Back

The equation y = (x + 2)^2 translates the graph of y = x^2 left 2 units.

Front

What does the equation y = |x - 3| represent in terms of horizontal shifts?

Back

The equation y = |x - 3| represents a horizontal shift of the absolute value graph y = |x| to the right by 3 units.

Front

If a graph is described as being shifted down 4 units, what is the general form of its equation?

Back

The general form of the equation would be y = f(x) - 4, where f(x) is the original function.

Front

What is the effect of adding a positive constant to a function?

Back

Adding a positive constant to a function results in a vertical shift of the graph upwards by that constant's value.

Front

What is the effect of subtracting a positive constant from a function?

Back

Subtracting a positive constant from a function results in a vertical shift of the graph downwards by that constant's value.

Front

How does the equation y = (x - 5)^2 transform the graph of y = x^2?

Back

The equation y = (x - 5)^2 translates the graph of y = x^2 right 5 units.

Front

What does the equation y = (x + 4)^2 indicate about the graph's transformation?

Back

The equation y = (x + 4)^2 indicates that the graph of y = x^2 is shifted left 4 units.

Front

If the graph of y = f(x) is shifted right 3 units, what is the new equation?

Back

The new equation would be y = f(x - 3).