Pre-Calc+Notes

Chapter 1: Functions and Their Graphs //__**1. Functions and Their Graphs**__// - A **relation** is a correspondance between two sets where each element in the first set is called the **domain,** corresponds to //at least// one element in the second set, called the **range**. - A **function** is a correspondance between two sets where each element in the first set, called the **domain**,corresponds to //exactly// one element in the second set, called the **range.** //__**2. Determining Whether an Equation is a Function**__// **//Vertical Line Test//** **Given the graph of an equation, if any vertical line that can be** **drawn intersect the graph at no more than one point, the equation** **defines a function of x. This test is called the vertical line test.** **//__3. Function Notation__//** **Function Notation:** f(x) - 2x + 5 x = independent variable f = mapping f(x) = dependent variable f(x) = 2x + 5 **//__4. Find Function Values from the Graph of a Function__//** - To determine values from the graph of a function, simply look at the values requested within the function. - For example: a. find f(0) (0) is the x axis //**__5. Determining the Domain of a Function__**// - Write the original equation - Determine any restrictions of the values of x - Solve the restriction equation - State the domain restrictions. - Write the domain in interval notation **//__6. Function Vs. Relation__//** - A function relates each element in the first set to **exactly one** in the second set. - A relation is a correspondence in which each element in the first set relates to **at least one** in the second set.