Absolute Value Graphing

Front

What is the definition of absolute value?

Back

The absolute value of a number is its distance from zero on the number line, regardless of direction. It is denoted as |x|.

Front

What does the graph of y = |x| look like?

Back

The graph of y = |x| is a V-shaped graph that opens upwards, with its vertex at the origin (0,0).

Front

How does the equation y = |x - h| + k affect the graph?

Back

The value 'h' shifts the graph horizontally, and 'k' shifts it vertically. The vertex of the graph is at the point (h, k).

Front

What is the vertex of the graph y = |x + 3| - 2?

Back

The vertex is at the point (-3, -2).

Front

How does the coefficient in front of the absolute value affect the graph?

Back

A positive coefficient stretches the graph vertically, while a negative coefficient reflects it across the x-axis.

Front

What is the effect of adding a constant outside the absolute value function?

Back

Adding a constant outside the absolute value function shifts the graph vertically. For example, y = |x| + 3 shifts the graph up by 3 units.

Front

What is the equation of the graph that opens downwards?

Back

The equation is of the form y = -a|x - h| + k, where 'a' is positive.

Front

What does the equation y = 2|x| represent?

Back

This represents a vertical stretch of the basic absolute value function, making the V-shape narrower.

Front

How do you find the x-intercepts of the graph y = |x - 2|?

Back

Set y = 0 and solve |x - 2| = 0, which gives x = 2.

Front

What is the significance of the vertex in an absolute value graph?

Back

The vertex is the highest or lowest point of the graph, depending on whether it opens upwards or downwards.