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# Chapter 1: Functions

### Functions

What is a variable? A variable is a symbol that can be replaced by any member of a set of numbers or objects.
What is an algebraic expresion? When numbers and variables are combined using the operations of arithmetic; the result is called an algebraic expression.
What is an algebraic sentance? An algebraic sentance consists of expressions related with a verb.
EX 1: Express the cost of y cans of orange juice at x per can. Solution 1: Use a special case. 5 cans at 600 per can would cost 5 X 60 cents= 300 cents = \$3.00. That suggests multiplication. So y cans at x cents per can will cost xy cents.
What rules must you use in order to evaluate expressions? Rules for Order of Operation: 1. Perform operations with parenthesis, brackets, or grouping symbols. 2. Take powers 3. Muliply and divide in order from left to right. 4. Add and subtract in order from left to right.
What is a function? A function is corresponding or pairing between two variables such that each value of first(independent) variable corresponds to exactly one value of the second(dependent) variable.
What is the domain of a function? It's the set of values which are allowable subsitutions for the independent variable.
What is the range of a function? It's the set of values of the dependent variable that can result from the subsitutions for the independent variable.
EX: Give the domain and range of the function. The domain is the set of all values of the independent variable Y. So the domain is {1981,1982,1983,1984,1985,1986,1987,1988,1989,1990,1991}. The range is {42.7,57.8,86.1,94.6,97.4,98.7,99.0,98.8,99.4}
What is arrow notation? Like Euler's notation, mapping notation states both the name of the function and independent variable.
EX: The sum of the angle measures in a polygon with n sides is given by the formula S= 180(n-2). Rewrite the formula a. using Euler's notation b. using mapping notation Solution: The independent variable n. Pick a name for the function, say f. Replace the dependent variable with f(n) a. f(n)=180(n-2) b. f:n arrow 180(n-2) Notice that S=f(n)
What is the Thereom( Vertical-Line Test for Functions)? No vertical line intersects the graph of a function in more than one point.
What is the Distributive Property? For all real numbers a, b and c. c(a+b)=ca+cb
Ex:Suppose f(m) = 6m - (5-9m). For what value of m is f(m)=13? Solution: Solve 6m-(5-9m)=13 6m-5+9m=13 Opposite of a Sum Theorem 15m-5=13 Add like Terms 15m=18 m=18/15=6/5 Muliply each side by 1/15
Formula: Consider the formula d=rt where d is the distance an object travels, r is the rate at which it travels, and t is the time the object travels. Suppose you wanted to calculate the distance traveled on a airplane going at rate of 650 miles/hour for 2.5 hours. d=(650 miles/hour) X (2.5 hours) = 1625 miles
Solved for a variable Notice that when a formula is solved for a variable, that variable has a coefficent and an exponent equal to one. That variable is said to be written in terms of the others.
What is an explicit formula? The sentance t(n)=n(n+1)/2 is called an explicit formula.
EX: What is the 20th triangular number? Solution: To find the 20th term in the sequence, evaluate t(20) t(20)=20(20+1)/2=20 X 21/2 The 20th triangular number is 210.
What is a recursive formula? A sequence is a set of statements that a. indicates the first term(or first few terms)and b. tells how the nth term is relation to one or more previous terms.
Created by: kmalone30