## Key Equations

 Constant function $f\left(x\right)=c$, where $c$ is a constant Identity function $f\left(x\right)=x$ Absolute value function $f\left(x\right)=|x|$ Quadratic function $f\left(x\right)={x}^{2}$ Cubic function $f\left(x\right)={x}^{3}$ Reciprocal function $f\left(x\right)=\frac{1}{x}$ Reciprocal squared function $f\left(x\right)=\frac{1}{{x}^{2}}$ Square root function $f\left(x\right)=\sqrt{x}$ Cube root function $f\left(x\right)=\sqrt[3]{x}$

## Key Concepts

• A relation is a set of ordered pairs. A function is a specific type of relation in which each domain value, or input, leads to exactly one range value, or output.
• Function notation is a shorthand method for relating the input to the output in the form $y=f\left(x\right)$.
• In table form, a function can be represented by rows or columns that relate to input and output values.
• To evaluate a function we determine an output value for a corresponding input value. Algebraic forms of a function can be evaluated by replacing the input variable with a given value.
• To solve for a specific function value, we determine the input values that yield the specific output value.
• An algebraic form of a function can be written from an equation.
• Input and output values of a function can be identified from a table.
• Relating input values to output values on a graph is another way to evaluate a function.
• A function is one-to-one if each output value corresponds to only one input value.
• A graph represents a function if any vertical line drawn on the graph intersects the graph at no more than one point.
• A graph represents a one-to-one function if any horizontal line drawn on the graph intersects the graph at no more than one point.

## Glossary

dependent variable
an output variable
domain
the set of all possible input values for a relation
function
a relation in which each input value yields a unique output value
horizontal line test
a method of testing whether a function is one-to-one by determining whether any horizontal line intersects the graph more than once
independent variable
an input variable
input
each object or value in a domain that relates to another object or value by a relationship known as a function
one-to-one function
a function for which each value of the output is associated with a unique input value
output
each object or value in the range that is produced when an input value is entered into a function
range
the set of output values that result from the input values in a relation
relation
a set of ordered pairs
vertical line test
a method of testing whether a graph represents a function by determining whether a vertical line intersects the graph no more than once

## Contribute!

Did you have an idea for improving this content? We’d love your input.