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# College Alegbra Day 9 notes 12458

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This 10 page Class Notes was uploaded by Corina Johnson on Sunday February 21, 2016. The Class Notes belongs to 12458 at University of Houston taught by Moses Sosa in Spring 2016. Since its upload, it has received 12 views. For similar materials see College Alegbra in Math at University of Houston.

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Date Created: 02/21/16

Math 1310 Section 3.1: Functions‐ Basic Ideas The rest of this course deals with functions. Definition: A function, f, is a rule that assigns to each element x in a set A exactly one elements, called f(x), in a set B. Functions are so important that we use a special notation when working with them. We’ll write f(x) to denote the value of function f at x. We read this as “f of x.” We can use letters other than f to denote a function, so you may see a function such as g(x), h(x) or P(x). Definition: The set A is called the domain and is the set of all valid inputs for the function. Definition: The set B is called the range and is the set of all possible values of f(x) as x varies throughout the domain. Sets A and B will consist of real numbers. Example 1: a. Given: Domain f Range 1 A 2 B C Is f a function? b. Given: Domain g Range 1 A 2 B 3 C Is g a function? Next we’ll consider some things you’ll need to be able to do when working with functions. First, you’ll need to be able to evaluate all types of functions when given a specific value for the variable. 1 Section 3.1: Functions‐Basic Ideas ▯ Example 2: Let ▯ ▯ ▯ ▯ ▯4▯ Calculate a. ▯ ▯3 ▯ b. ▯2▯ ▯ ▯ ▯ c. ▯ 3▯ ▯ d. ▯▯▯ ▯ 2▯ 2▯ ▯ 6,▯ ▯ ▯2 Example 3: Suppose ▯ ▯ ▯ ▯ ▯ ▯ ▯ ▯ ▯2▯▯3,▯▯▯2 . Calculate the following a. ▯ ▯5 ▯ b. ▯ ▯2 ▯ 2 Section 3.1: Functions‐Basic Ideas c. ▯▯3▯ Popper 1: Given the function ▯ ▯ ▯▯▯ ▯ ▯ ▯ ▯2▯▯3, find f(‐1). 4 ‐ ) a 0 ) b 6 ‐ ) c 3 ‐ ) d 1 ‐ ) e Popper 3: Given the following function, find f(2) and f(‐2). x x1 4 fx() x 2 1 x 4 3 1 x a) f(2) = 4 and f(‐2) = ‐4 b) f(2) = 4 and f(‐2) = 3 c) f(2) = 3 and f(‐2) = ‐4 d) f(2) = 4 and f(‐2) = ‐1 e) f(2) = 3 and f(‐2) = ‐3 3 Section 3.1: Functions‐Basic Ideas Finding the Domain of a Function Recall: The domain is the set of all real numbers for which the expression is defined as a real number. Exclude from a function’s domain real numbers that cause division by zero or real numbers that result in an even root of a negative number. We express the set of real numbers as (‐ ∞, ∞). The domain of any polynomial function is (‐∞, ∞). Example 4: Find the domain of each function below and express your answer in interval notation. a. f(x) = ‐17 b. f(x) = 3x – 4 c. ▯ ▯ ▯ 5▯ 2▯ ▯ 8 x 1 d. f ( ) 2x 6 4 Section 3.1: Functions‐Basic Ideas e. ▯ ▯ ▯ ▯ ▯ ▯16 ▯ ▯4▯▯12 f. ▯ ▯ ▯ ▯ √ g. ▯ ▯ ▯ ▯▯4 √ ▯ h. ▯ ▯ ▯ √ 2▯ ▯ 4 i. ▯ ▯ ▯ ▯▯√ 42 ▯ 2▯ 5 Section 3.1: Functions‐Basic Ideas Popper 6: Find the domain of the function and express your answer in interval notation. ▯▯2 ▯ ▯ ▯ ▯▯3 ) a ))(, ) b ) 3)(3 ,(, ) 0)(0, ) c ) d ) 3)(3, e) None of the above 6 Section 3.1: Functions‐Basic Ideas Math 1310 Section 3.2: Functions and Graphs You can answer many questions given a graph. Definition: The graph of a function f (x) is the set of points (x, y) whose x coordinates are in the domain of f and whose y coordinates are given by y = f (x). First, does the graph represent a function? To answer this, you will need to use the vertical line test (VLT). The Vertical Line Test: If you can draw a vertical line that crosses the graph more than once, it is NOT the graph of a function. Example 1: Determine if the graph represents a function: a. b. 1 Section 3.2: Functions‐and Graphs Definition: An equation defines y as a function of x if when one value for x is substituted in the equation, exactly one value for y is returned. Example 2: Does the following equation define y as a function of x? ▯ ▯▯▯ ▯4 1. Solve for y. 2. For each value x, do we get exactly one value for y back? b. ▯ ▯▯ ▯9 ▯ 1. Solve for y. 2. For each value x, do we get exactly one value for y back? Example 3: Find the domain and range of the function whose graph is shown. : n i a m o D ____________________ : e g n a R _____________________ 2 Section 3.2: Functions‐and Graphs You’ll also need to be able to graph functions. For now, you can do so by plotting points. But… YOU MUST KNOW THESE FUNCTIONS AND GRAPHS 2 3 f(x) x f(x) x 1 f(x) x 4 Section 3.2: Functions‐and Graphs Example 4: Suppose ▯ ▯ ▯ 2▯ ▯ 5. State the domain of the function and graph it. Example 5: Suppose f (x) = 4x ‐1, ‐1< x < 2 . Graph the function. 5 Section 3.2: Functions‐and Graphs

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