Assessment and Learning in Knowledge Spaces (ALEKS) Practice Exam

Which best describes an absolute value equation?

1. A linear equation with one variable

2. A V-shaped graph that points upward or downward

3. An equation with no real solutions

4. A polynomial equation of degree two

The correct answer is: A V-shaped graph that points upward or downward

An absolute value equation is best described by its characteristic V-shaped graph. This type of equation typically takes the form |x| = a, where a is a real number. The nature of the absolute value function is such that it measures the distance from zero, resulting in two distinct linear pieces when graphed. If the absolute value equals a positive number, the graph will have two intersection points with the line y = a, thereby forming a V-shape that points either upward or downward, depending on the specific equation. However, generally, the graph will point upward, creating a characteristic V-shape that clearly denotes the relationship of the values involved. In contrast, while an absolute value equation can be linear and involve one variable, it is more accurately represented by the V-shape graph that defines how absolute values behave. It's also possible for absolute value equations to have no solutions, but this depends on the specific equation being analyzed and does not define the concept of absolute value itself. Finally, an absolute value equation does not fit the mold of a polynomial of degree two, as it is not necessarily quadratic but rather a piecewise linear function shaped by absolute values.