3.8 Chapter Summary
In this chapter, we studied the concept of distance from a mathematical perspective.
|Introduction||The distance between two objects is measured using a mathematical symbol known as the absolute value.|
|Absolute Value Definition||The absolute value function, |x|, is a piecewise defined function; it is defined differently on different parts of its domain:
Graphically, it looks like:
|Distance from the Origin||If a≥0, then to solve the equation |x|=a, we can find x by either
If a<0, then the equation |x|=a has no solution.
|Solving Absolute Value Equalities||To solve more complicated absolute value equalities, we can follow the basic process that we previously studied. However, since the expression in the absolute value could be very complicated, in these cases, it's better to find the solution algebraically as opposed to using the number line method.|
|Distance Between Two Points||In English, |a-b| represents the distance between the points a and b.|
|Solving Less Than Inequalities||
|x| < a means that x is less than "a" units from the origin.
|Sovling Greater Than Inequalities||
|x|> a means that x is more than "a" units from the origin.