Key Concepts

• Formulas for specific types of applications containing more than one variable may be solved for an unknown variable by substituting known values and solving the formula for the unknown variable.
• Functions containing radicals may be graphed by substituting input values and solving for the coordinating output value to create a graph of points existing on the graph. After plotting enough points to obtain the shape of the graph, draw a smooth curve between them.
• Work [latex]W[/latex], rate [latex]r[/latex], and time [latex]t[/latex] may be related by the formulas [latex]W=rt,\text{ }t=\dfrac{W}{r}\text{, and }r=\dfrac{W}{t}[/latex]
• Proportions, equations of the form [latex]\dfrac{a}{b}=\dfrac{c}{d}[/latex], are helpful for setting up relationships in applications. Solve by cross-multiplying or by multiplying both sides of the equation by the reciprocal of one.

Glossary

proportion

a statement of the equality of two ratios

radical formula

an equation used in certain applications that contains at least one radical expression (a variable expression using a radical such as a square or cube root)

rational formula

an equation used in certain applications that contains at least one rational expression (a variable expression in fraction form)