Product Rule for Exponents
Decimal Numbers and Fractions
The Slope of a Line
Adding and Subtracting Square Roots
Factoring the Difference of Two Squares
Linear Systems of Equations with Infinitely Many Solutions
Axis of Symmetry and Vertices
Types of Linear Equations
Sum of Squares
Subtract Fractions with Unlike Denominators
Solving equations
Solving Exponential Equations
Multiplying by 715
Adding and Subtracting Functions
Negative and Fractional Powers
Graphing Linear Equations in Two Variables
Solving Equations That Contain Rational Expressions
Dividing Polynomials
Polynomials in Several Variables
Multiplying Polynomials
Adding and Subtracting Fractions
Solving Absolute Value Inequalities
Simplifying Complex Fractions
Evaluating Rational Functions
Product Rule for Radicals
Domain and Range of a Function
Solving Linear Equations
Dividing Whole Numbers by Fractions
Reducing Rational Expressions to Lowest Terms
Dividing Polynomials
Factoring by Substitution
Dividing a Polynomial by a Monomial
Linear Inequalities
Adding and Subtracting Complex Numbers
What the Vertex Form of a Quadratic can tell you about the graph
Finding x
Adding and Subtracting Fractions with Like Denominators
Adding and Subtracting Fractions
Solving Equations
Graphing Linear Equations
Greatest Common Factors
Exponential Functions
Methods for Solving Quadratic Equations
Factoring Trinomials with Leading Coefficient Not 1
Properties of Natural Logs
Steps for Solving Linear Equations
Multiplying Binomials
Factoring Trinomials
Adding and Subtracting Mixed Numbers with Different Denominators
Simplifying Complex Fractions
Sum or Difference of two Cubes
Multiplying by 858
Graphing Quadratic Equations
Rational Expressions
Graphing Vertical Lines
Dividing Fractions
Multiplying Numers
Multiplying Two Numbers Close to but greater than 100
Factoring Trinomials
Equivalent Fractions
Finding the Least Common Multiple
Factoring Rules
Laws of Exponents
Multiplying Polynomials
Dividing Rational Expressions
Evaluating Polynomial Functions
Equations Involving Rational Exponents
Adding and Subtracting Fractions
Factoring Polynomials by Finding the Greatest Common Factor
Rules for Integral Exponents
Rationalizing the Denominator
Ratios and Rates
Factoring Trinomials
Multiplying Polynomials
Point-Slope Form of a Line
Multiplying Decimals
Solving Right Triangles
Solving Equations with One Radical Term
Adding and Subtracting Mixed Numbers
Adding and Subtracting Polynomials
Division Property of Square and Cube Roots
Inverse Functions
Factoring Trinomials
Writing Percents as Fractions
Solving Equations with One Radical Term
Graphing Systems of Inequalities
Multiplying and Dividing Monomials
Roots - Radicals 2
Solving Linear Systems of Equations
Multiplying and Factoring
Solving Equations with Rational Expressions

Domain and Range of a Function

You have seen that a function is a rule that assigns to each input number, x, exactly one output number, y.

The set of x-values is called the domain of the function.

The set of y-values is called the range of the function.

Example 1

Given the function: y = x2

a. Find the domain.

b. Find the range.


a. To find the domain, ask yourself, “What is x allowed to be?”. Since we can square any real number, the domain of y = x2 is all real numbers.

b. To find the range, ask yourself, “What results when we square a real number?” Squaring a real number always results in 0 or a positive real number. Thus, the range of y = x2 is y 0.

We can see from the graph that the smallest value of y is 0.

The domain and range of a function can be expressed in several different ways.

Represent the domain of the function shown in the graph:

a. Using words.

b. Using inequality symbols.

c. Using a number line.

d. Using interval notation.


The function consists of all the ordered pairs on the line. The x-values start at -6 and go up to, but do not include, 4.

a. The domain is all real numbers between -6 and 4, including -6.

Or, we could say “the domain is all real numbers greater than or equal to -6 and less than 4.”

b. -6 ≤ x < 4



Remember, a closed circle, , on a graph means a point is included in the solution; an open circle, , means the point is not included.

d. Interval notation indicates the domain by stating the end points of an interval.

If an end point is included, we use a square bracket, [ or ]; if the end point is not included, we use a parenthesis, ( or ). For the function shown, we write the domain as [-6, 4):

• the domain starts at and includes -6, so we use a [ next to -6.

• the domain ends at, but does not include, 4, so we use a ) next to 4.


Interval notation can look like an ordered pair. For example, (2, 5) can have two different meanings depending on the context in which it is used:

• If we are talking about a domain, then the interval (2, 5) represents all the values between 2 and 5 (not including 2 or 5).

• If we are talking about a point on the xyplane, then the ordered pair (2, 5) represents the coordinates of a point. The x-coordinate is 2 and the y-coordinate is 5.