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 on the coordinate plane. For example, in the function y = f(x) + k, the graph shifts up k units if k > 0 and down 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 on the coordinate plane. In the function y = f(x - h), the graph shifts right h units if h > 0 and left h units if h < 0.

Front

How does the equation y = (x - 3)² transform the graph of y = x²?

Back

The equation y = (x - 3)² translates the graph of y = x² to the right by 3 units.

Front

What does the equation y = |x + 5| represent in terms of horizontal shifts?

Back

The equation y = |x + 5| represents a horizontal shift of the absolute value graph to the left by 5 units.

Front

If the equation is y = x² + 5, what transformation has occurred?

Back

The equation y = x² + 5 represents a vertical shift of the graph of y = x² upwards by 5 units.

Front

What is the effect of adding a negative value to the x variable in a function?

Back

Adding a negative value to the x variable in a function, such as y = f(x + h), results in a horizontal shift to the left by h units.

Front

Describe the transformation of the graph y = -x² - 5.

Back

The graph y = -x² - 5 is a vertical shift downwards by 5 units and a reflection across the x-axis.

Front

What does the term 'translation' mean in graph transformations?

Back

Translation refers to shifting a graph in the coordinate plane without changing its shape or orientation.

Front

How does the equation y = |x| - 3 transform the graph of y = |x|?

Back

The equation y = |x| - 3 translates the graph of y = |x| downwards by 3 units.

Front

What is the transformation represented by y = (x + 2)²?

Back

The equation y = (x + 2)² translates the graph of y = x² to the left by 2 units.