Math 1351-011 August 29, 2007 1
Announcements
•Homework 1 due today.
•Homework 2 due next Friday in class.
•In class quizzes during discussion sections begin next
week.
TTU Department of Mathematics & Statistics
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Math 1351-011: Functions and Graphs - Prof. Victoria Ellen Howle, Study notes of Mathematics
The concept of functions and graphs in mathematics 1351-011 at texas tech university. It covers definitions, properties, evaluating functions, piece-wise defined functions, and an application of the formula for an object falling in a vacuum. Students are expected to understand functions as rules that assign unique outputs to inputs, their domains and ranges, and how to evaluate functions for specific inputs.
Typology: Study notes
Pre 2010
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Announcements
- Homework 1 due today.
- Homework 2 due next Friday in class.
- In class quizzes during discussion sections begin next week.
Section 1.3 — functions and graphs
- Definitions: A function f is a rule that assigns to each element x of a set X a unique element y of a set Y. The element y is called the image of x under f and is denoted f (x). The set X is called the domain of f , and the set of all images of elements of X is called the range of the function.
- A function f can be thought of as the set of ordered pairs (x, y) where each member x of the domain is associated with exactly one member y = f (x) of the range.
- A function assigns a unique “output” to each legitimate “input”
- Evaluating a function means to find the value of f for a particular value in the domain.
- Example: f (x) = 2x^2 − x
Find f (x + h)
Find f^ (x+h h)− f^ (x),
where x and h are real numbers and h 6 = 0.
- f^ (x+h h)− f^ (x) is called a difference quotient. It will be important in chapter 3 (derivatives).
Piece-wise defined functions
- Some functions are defined differently on different parts of their domain.
- Example:
f (x) =
x sin x if x < 2 3 x^2 + 1 if x ≥ 2
- Find f ( π 2 ) and f (2):
- Domain of f is assumed to be the set of real numbers for which the function is defined (unless otherwise specified).
- Examples: find the domain: f (x) = 2x − 1 g(x) = 2x − 1 , x 6 = − 3 h(x) = (2x− x1)(+3x+3) F (x) =
x + 2 G(x) = (^5) −cos^4 x
- Function equality: Two functions f and g are equal if and only if 1. f and g have the same domain 2. f (x) = g(x) for all x in the domain