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Math 141Notes - y is the value of the function f at x The...

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Math 141 (Calculus 1) Chapter 1 Notes Functions and Limits Functions and Their Representations Objectives: Students should be able to: 1. Find the domain and range of a function 2. Determine on what interval a function is increasing or decreasing 3. Evaluate a function for given values of the independent variable 4. Evaluate the difference quotient for a given function Definition: Let A and B be two sets. A function f from set A to set B is a rule that assigns to each element x in a set A exactly one element, called f( x ), in set B. Examples: 1. f( x ) = 0.2 x + 5: In this case the domain A is the set of real numbers that x can attain, and B is the set of unique values f( x ) corresponding to each x in set A. 2. a(r) = π r 2 : In this case A is the set of values that the radius r can attain, and B is the set of areas a(r) corresponding to each radii in set A. 3. The set A is called the domain of the function. The domain can also be thought of as the set of all input values. The number f( x ) (which is sometimes called
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Unformatted text preview: y ) is the value of the function f at x . The range of the function f is the set of all possible values of f( x ) as x varies throughout the domain. The range can also be thought of as the set of output values. Example: Find the domain and range of the functions a) b) Four possible ways to represent a function are as follows: 1. Verbally (by a description in words) 2. Numerically (by a table of values) 3. Visually (by graph) 4. Algebraically (by an explicit formula) Note that the graph of a function is a curve in the x-y plane. A curve in the x-y plane is the graph of a function of x if and only if no vertical line intersects the curve more than once. Work # 2, & 4 on page 8, # 20, 28, 37 on page 9 A Catalog of Essential Functions Objectives: Students should be able to You should be familiar with the graphs of the following commonly occurring functions. 1. Linear functions: f( x ) = m x + b. What does m represent? Explain what it means. 2....
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