Graphing Absolute Value Equations

Front

What is the definition of an absolute value function?

Back

An absolute value function is a function that returns the non-negative value of a number, defined as f(x) = |x|. It measures the distance of x from 0 on the number line.

Front

What is the general form of an absolute value equation?

Back

The general form of an absolute value equation is y = 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 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 graphs?

Back

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

Front

How do you determine the vertex of the absolute value function y = a|bx + c| + d?

Back

The vertex can be found at the point (-c/b, d). This is the point where the expression inside the absolute value equals zero.

Front

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

Back

The term 'c' represents a horizontal shift. If 'c' is positive, the graph shifts to the left; if 'c' is negative, it shifts to the right.

Front

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

Back

The term 'd' represents a vertical shift. If 'd' is positive, the graph shifts upwards; if 'd' is negative, it shifts downwards.

Front

How do you graph the absolute value function y = |x|?

Back

To graph y = |x|, plot the vertex at (0,0) and draw two lines: one with a positive slope to the right and one with a negative slope to the left, forming a 'V' shape.

Front

What is the equation of the graph that opens downwards and is shifted down by 1 unit?

Back

The equation is y = -|x| - 1.

Front

How do you identify the transformations applied to the graph of y = |x| to get to y = |x - 2| + 3?

Back

The graph is shifted right by 2 units and up by 3 units.