Key Concepts & Glossary

Key Equations

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

 
 

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 [latex]y=f\left(x\right)[/latex].
  • In tabular 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.
  •  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.
  • The graph of a one-to-one function passes the horizontal line test.
 
 

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