Algebra Tutorials!  
Saturday 15th of June
Rotating a Parabola
Multiplying Fractions
Finding Factors
Miscellaneous Equations
Mixed Numbers and Improper Fractions
Systems of Equations in Two Variables
Literal Numbers
Adding and Subtracting Polynomials
Subtracting Integers
Simplifying Complex Fractions
Decimals and Fractions
Multiplying Integers
Logarithmic Functions
Multiplying Monomials
The Square of a Binomial
Factoring Trinomials
The Pythagorean Theorem
Solving Radical Equations in One Variable
Multiplying Binomials Using the FOIL Method
Imaginary Numbers
Solving Quadratic Equations Using the Quadratic Formula
Solving Quadratic Equations
Order of Operations
Dividing Complex Numbers
The Appearance of a Polynomial Equation
Standard Form of a Line
Positive Integral Divisors
Dividing Fractions
Solving Linear Systems of Equations by Elimination
Multiplying and Dividing Square Roots
Functions and Graphs
Dividing Polynomials
Solving Rational Equations
Use of Parentheses or Brackets (The Distributive Law)
Multiplying and Dividing by Monomials
Solving Quadratic Equations by Graphing
Multiplying Decimals
Use of Parentheses or Brackets (The Distributive Law)
Simplifying Complex Fractions 1
Adding Fractions
Simplifying Complex Fractions
Solutions to Linear Equations in Two Variables
Quadratic Expressions Completing Squares
Dividing Radical Expressions
Rise and Run
Graphing Exponential Functions
Multiplying by a Monomial
The Cartesian Coordinate System
Writing the Terms of a Polynomial in Descending Order
Quadratic Expressions
Solving Inequalities
Solving Rational Inequalities with a Sign Graph
Solving Linear Equations
Solving an Equation with Two Radical Terms
Simplifying Rational Expressions
Intercepts of a Line
Completing the Square
Order of Operations
Factoring Trinomials
Solving Linear Equations
Solving Multi-Step Inequalities
Solving Quadratic Equations Graphically and Algebraically
Collecting Like Terms
Solving Equations with Radicals and Exponents
Percent of Change
Powers of ten (Scientific Notation)
Comparing Integers on a Number Line
Solving Systems of Equations Using Substitution
Factoring Out the Greatest Common Factor
Families of Functions
Monomial Factors
Multiplying and Dividing Complex Numbers
Properties of Exponents
Multiplying Square Roots
Adding or Subtracting Rational Expressions with Different Denominators
Expressions with Variables as Exponents
The Quadratic Formula
Writing a Quadratic with Given Solutions
Simplifying Square Roots
Adding and Subtracting Square Roots
Adding and Subtracting Rational Expressions
Combining Like Radical Terms
Solving Systems of Equations Using Substitution
Dividing Polynomials
Graphing Functions
Product of a Sum and a Difference
Solving First Degree Inequalities
Solving Equations with Radicals and Exponents
Roots and Powers
Multiplying Numbers
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Functions and Graphs

Definition of a Function

We often work with two quantities that are related.

For example, let’s say you put gas in your car. The total cost of the gas is related to the number of gallons of gas you buy.

Suppose gas costs $1.50 per gallon. Then, the relationship between the cost in dollars, y, and the number of gallons, x, is given by: y = 1.50x

The equation y = 1.50x is an example of a function.


Definition — Function

A function is a rule that assigns to each number in one set exactly one number in another set.


The function y = 1.50x is a rule that says to start with a number, represented by x, and to multiply that number by 1.50. The result is the number represented by y. The ordered pair, (x, y) is said to satisfy the function.

For example, the ordered pair (2, 3) satisfies the function y = 1.50x. This is because replacing x with 2 and y with 3 results in a true statement:

Is 3 = 1.50 · 2 ?

Is 3 = 3 ? Yes


Example 1

In the function y = 1.50x, the variable y represents the cost in dollars and x represents the number of gallons of gas purchased. Find the cost of 6 gallons of gas.


In the function, y = 1.50x, substitute 6 for x and simplify.

Let x = 6


y = 1.50 (6)

y = 9.00

So, the cost of 6 gallons of gas is $9.00.

The ordered pair (6, 9) satisfies the function y = 1.50x.

The two sets related by a function have special names. The first set is called the domain of the function. A number in this set is called an input. The input is usually represented by the letter x.

The second set is called the range of the function. A number in this set is called an output. The output is often represented by the letter y.


You can think of a function as a machine that assigns to each input number, x, exactly one output number, y.

Here are three more examples of functions:

Absolute Value




Square Root


y = - x2 - 6 y = 4|x| - 8

Function Notation

Functions can also be written in function notation, a special notation that uses letters such as f, g, and h.

For example, when x is the input, the output may be written as f(x). This is read, “f of x”. This notation shows that each output value is related to each input value by the function, f.

For example,

y = - x2 - 6 is equivalent to f(x) = - x2 - 6

y = 4|x| - 8 is equivalent to g(x) = 4|x| - 8

is equivalent to

If we are given a value for x, we can find the corresponding value of the function, f(x).


In the past, you have used parentheses to indicate multiplication. Thus, f(x) could also be interpreted as the variable f multiplied by the variable x. The only way to tell if f(x) means function or multiplication is to look at the context in which it is used.


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