1 / 12

120 likes | 307 Vues

Calculus I (MAT 145) Dr. Day Thur sday Jan 17,2013. Function Characteristics (continued) (1.1 – 1.3) Assignments. 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

Télécharger la présentation
## Calculus I (MAT 145) Dr. Day Thur sday Jan 17,2013

**An Image/Link below is provided (as is) to download presentation**
Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.
Content is provided to you AS IS for your information and personal use only.
Download presentation by click this link.
While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.
During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

**Calculus I (MAT 145)Dr. Day Thursday Jan 17,2013**• Function Characteristics (continued) (1.1 – 1.3) • Assignments 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 Functions 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. MAT 145**One-to-One Functions**Afunction f is a rule that assigns to each element x in a set A exactly one element, called f(x), in a set B. 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. MAT 145**Domain and Range of Functions**Afunction f is a rule that assigns to each element x in a set A exactly one element, called f(x), in a set B. • 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 MAT 145**Representations of Functions**Graphsprovide 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. MAT 145**Representations of Functions**Represent each of the functions above: • in a table • verbally State the domain and range for each function. MAT 145**Function Notation**• What does f(x) = 3x + 5 represent? • Using y = f(x) as just described, determine and simplify each of the following. • f(2) (b) f(−4) (c) f() (d) f(x-1) • f(2x+4) (f) f(t2+7t) (g) f(f(x)) (h) f(x + h) (i) f(x + h) – f(x) MAT 145**Families of Functions**Algebraic—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 MAT 145**Operating on Functions**Algebra of functions: apply one or more of the four basic operations (+,−,,) to two or more functions. Composition of functions: putting together two ormore functions in a particular way. When two functions are composed, one is evaluated within the other. MAT 145**Reminders/Assignments**• Assignments • PIP Packet #54 • WebAssign: Sec 1.2 and 1.3 • Quiz #3: function characteristics (1.1 to 1.3) MAT 145

More Related