Absolute Value Functions Graphs

Front

What is the definition of an absolute value function?

Back

An absolute value function is a function that contains an algebraic expression within absolute value symbols, which measures the distance of a number from zero on the number line, always resulting in a non-negative value.

Front

What is the general form of an absolute value function?

Back

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

Front

How does the value of 'a' affect the graph of an absolute value function?

Back

The value of 'a' affects the vertical stretch or compression and the direction of the graph. If 'a' is positive, the graph opens upwards; if 'a' is negative, it opens downwards.

Front

What does the term 'vertex' refer to in the context of absolute value functions?

Back

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

Front

How do you find the vertex of the function f(x) = a|bx + c| + d?

Back

The vertex can be found at the point (-c/b, d) in the coordinate plane.

Front

What effect does changing 'c' have on the graph of an absolute value function?

Back

Changing 'c' shifts the graph horizontally. If 'c' is positive, the graph shifts to the left; if 'c' is negative, it shifts to the right.

Front

What effect does changing 'd' have on the graph of an absolute value function?

Back

Changing 'd' shifts the graph vertically. If 'd' is positive, the graph shifts up; if 'd' is negative, it shifts down.

Front

What is the graph of the function y = |x|?

Back

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

Front

How do you graph the function y = |x + 2| + 1?

Back

1. Identify the vertex at (-2, 1). 2. Plot points on either side of the vertex. 3. Draw a V-shaped graph opening upwards.

Front

What is the effect of a negative sign in front of the absolute value, such as in y = -|x|?

Back

The negative sign reflects the graph across the x-axis, resulting in an upside-down V shape.