We've updated our
Privacy Policy effective December 15. Please read our updated Privacy Policy and tap

Study Guides > MATH 1314: College Algebra

Key Concepts & Glossary

Key Concepts

  • The absolute value function is commonly used to measure distances between points.
  • Applied problems, such as ranges of possible values, can also be solved using the absolute value function.
  • The graph of the absolute value function resembles a letter V. It has a corner point at which the graph changes direction.
  • In an absolute value equation, an unknown variable is the input of an absolute value function.
  • If the absolute value of an expression is set equal to a positive number, expect two solutions for the unknown variable.
  • An absolute value equation may have one solution, two solutions, or no solutions.
  • An absolute value inequality is similar to an absolute value equation but takes the form A<B,AB,A>B, or AB|A|<B,|A|\le B,|A|>B,\text{ or }|A|\ge B\\. It can be solved by determining the boundaries of the solution set and then testing which segments are in the set.
  • Absolute value inequalities can also be solved graphically.

Glossary

absolute value equation
an equation of the form A=B|A|=B\\, with B0B\ge 0\\; it will have solutions when A=BA=B\\ or A=BA=-B\\
absolute value inequality
a relationship in the form A<B,AB,A>B,or AB|{ A }|<{ B },|{ A }|\le { B },|{ A }|>{ B },\text{or }|{ A }|\ge{ B }\\

Licenses & Attributions