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Calculus I (MAT 145)Dr. Day Wednesday Jan 16,2013
Connecting Change and Accumulation
Reminder: Course Resources Textbook WebAssign Instructor Website
Function Characteristics (1.1 – 1.3)
Assignments
Wednesday, January 16, 2013
MAT 145
MAT 145
Making Connections
Wednesday, January 16, 2013
CHANGE
ACCUMULATE
LIMITS
FUNCTIONS
CALCULUS!
PRE-CALCULUS!
MAT 145
Algebra Will Get You Every Time
Expanding and Factoring, Reducing Fractions, and Other Ways to Simplify Expressions
Solving Equations
Functions and Their Properties Linear Functions, Other Polynomial Functions,
Exponential Functions, Logarithmic Functions, Rational Functions, Trig Functions, and Others
Domain and Range, Asymptotes, Increasing and Decreasing Intervals, Extreme Values, End Behavior
Wednesday, January 16, 2013
MAT 145
Functions(PIP p5-8; Text section
1.1-1.3) Define
One-to-one functions
Domain and Range
Representations for Functions
Increasing and Decreasing Functions; Notation
Families of Functions
Operating on FunctionsWednesday, January 16, 2013
MAT 145
Functions
A function f is a rule that assigns to
each element x in a set A exactly
one element, called f(x), in a set B.
Wednesday, January 16, 2013
MAT 145
One-to-One Functions
A one-to-one function is a function for which each element y in set B corresponds to exactly one element x in set A.
Wednesday, January 16, 2013
A function f is a rule that assigns to
each element x in a set A exactly
one element, called f(x), in a set B.
MAT 145
Set A is the domain of the function.
Set B is the range of the function.
What does f(x) represent?
Limitations on a Domain and Range Wednesday, January 16, 2013
Domain and Range of Functions
A function f is a rule that assigns to
each element x in a set A exactly
one element, called f(x), in a set B.
MAT 145
Graphs provide a visual representation of the relationship between input (x) and output (y) by plotting ordered pairs (x,y), such that , y = f(x), on orthogonal (right-angled) axes.
Sketch the graphs and label at least three ordered pairs for these functions.
Wednesday, January 16, 2013
Representations of Functions
MAT 145
Represent each of the functions above:
in a tableverbally
State the domain and range for each function.
Wednesday, January 16, 2013
Representations of Functions
MAT 145
Increasing and Decreasing Functions
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MAT 145
Function NotationWhat does f(x) = 3x + 5
represent?
Using y = f(x) as just described, determine and simplify each of the following.
(a)f(2) (b) f(−4) (c) f() (d) f(x-1)
(e)f(2x+4) (f) f(t2+7t) (g) f(f(x))
(h) f(x + h) (i) f(x + h) – f(x)
Wednesday, January 16, 2013
MAT 145
Families of FunctionsAlgebraic—functions formed by using algebraic operations (+, -, x, ÷, nth root of a , a to the mth power , such that m and n are rational) on coefficients and variables
Polynomial (Constant, Linear, Quadratic, Cubic, Quartic, and others)
Power Root Rational
Transcendental—non-algebraic functions (i.e., those that “transcend” algebra)
Trigonometric Exponential Logarithmic
Others—Piecewise, Absolute Value, Greatest Integer, and others
Wednesday, January 16, 2013
MAT 145
Operating on FunctionsAlgebra of functions: apply one or more of the four basic operations (+,−,,) to two or more functions.
Wednesday, January 16, 2013
Composition of functions: putting together two or more functions in a particular way. When two functions are composed, one is evaluated within the other.
MAT 145
Course Resources Textbook WebAssign Calculators Instructor Website:
math.illinoisstate.edu/day/courses/current/145/www.html
Assignments PIP Packet #54 WebAssign : Intro to WebAssign WebAssign : Sec 1.1 and 1.2 Quiz #2: linear equations, function characteristics, words
to symbols
Reminders/Assignments
Wednesday, January 16, 2013
