Graphing Absolute Values

Front

What is the definition of an 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

How do you graph the absolute value function f(x) = |x|?

Back

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

Front

What effect does the coefficient in front of the absolute value have on the graph?

Back

A coefficient greater than 1 (e.g., 2|x|) vertically stretches the graph, while a coefficient between 0 and 1 compresses it. A negative coefficient reflects the graph across the x-axis.

Front

What does the expression f(x) = |x - 1| represent?

Back

This represents a translation of the basic absolute value function |x| to the right by 1 unit.

Front

How does the equation f(x) = |x| + 3 affect the graph of f(x) = |x|?

Back

This equation shifts the graph of f(x) = |x| upward by 3 units.

Front

What is the vertex of the graph of f(x) = 2|x - 1| + 1?

Back

The vertex is at the point (1, 1). This is the minimum point of the graph.

Front

How do you find the x-intercepts of the function f(x) = |x - 2|?

Back

Set the equation |x - 2| = 0. The x-intercept is at x = 2.

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, f(x) = |x| + 2 shifts the graph up by 2 units.

Front

What does the expression f(x) = -|x| indicate about the graph?

Back

This indicates that the graph is a reflection of the basic absolute value graph across the x-axis, creating an upside-down V shape.

Front

How do you determine the slope of the lines in the graph of f(x) = |x - 3|?

Back

The slope is 1 for x < 3 and -1 for x > 3, creating two linear segments that meet at the vertex (3, 0).