Graphing Absolute Value Functions

Front

What is an absolute value function?

Back

An absolute value function is a function that outputs the distance of a number from zero on the number line, regardless of direction. It is defined as f(x) = |x|.

Front

How does the graph of y = |x| look?

Back

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

Front

What effect does the equation y = |x - 3| have on the graph?

Back

The equation y = |x - 3| shifts the graph of y = |x| to the right by 3 units.

Front

What is the vertex of the function y = |x - 2|?

Back

The vertex of the function y = |x - 2| is at the point (2, 0).

Front

How does the equation y = |x| + 2 affect the graph?

Back

The equation y = |x| + 2 shifts the graph of y = |x| upwards by 2 units.

Front

What is the effect of a negative sign in front of an absolute value function, like y = -|x|?

Back

The negative sign reflects the graph of the absolute value function across the x-axis, making it open downwards.

Front

What is the general form of an absolute value function?

Back

The general form of an absolute value function is f(x) = a|bx + c| + d, where a, b, c, and d are constants.

Front

What does the 'a' value in the function f(x) = a|x| represent?

Back

The 'a' value represents the vertical stretch or compression of the graph. If |a| > 1, the graph stretches; if 0 < |a| < 1, it compresses.

Front

What does the 'd' value in the function f(x) = |x| + d represent?

Back

The 'd' value represents a vertical shift of the graph. If d > 0, the graph shifts up; if d < 0, it shifts down.

Front

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

Back

To find the x-intercepts, set y = 0: 0 = |x - 2|. This gives x - 2 = 0 or x - 2 = 0, so x = 2.