Slideshare uses cookies to improve functionality and performance, and to provide you with relevant advertising. If you continue browsing the site, you agree to the use of cookies on this website. See our User Agreement and Privacy Policy.

Slideshare uses cookies to improve functionality and performance, and to provide you with relevant advertising. If you continue browsing the site, you agree to the use of cookies on this website. See our Privacy Policy and User Agreement for details.

Like this presentation? Why not share!

518 views

394 views

394 views

Published on

mstfdemirdag.com

Published in:
Technology

No Downloads

Total views

518

On SlideShare

0

From Embeds

0

Number of Embeds

4

Shares

0

Downloads

11

Comments

0

Likes

1

No embeds

No notes for slide

- 1. FUNCTIONS
- 2. The Domain of a Function Example: The domain is the set of all real numbers for which the expression is defined as a real number. f(x) = 2x + 3 D=R g(x) = 2x + 3 D=R Example: f(x) = g(x) Example: 1 f (x ) = x −4 D = R – {4} f (x ) = x D = R+ g(x) = x f (x ) = 5 f (x ) = 2 − x 2x − 6 x f (x ) = 2 f (x ) = x 2 − 4 x −9 f (x ) = Equal Functions Two functions are equal if and only if their expressions and domains are equal. 2 x x D=R f(x) ≠ g(x) D = R – {0} Even and Odd Function A function is called even if f(-x) = f(x) A function is called odd if f(-x) = -f(x) Example: State whether each of the following functions are even or odd function. f(x) = 3x2 + 4 h(x) = 2x3 g(x) = x m(x) = x3 – 1
- 3. What is use of even and odd functions? Graph of a function is symmetric respect to y-axis if it is even. Graph of a function is symmetric respect to origin if it is odd. Example: Classify whether the following functions are even or odd.
- 4. Vertical Line Test: A graph is a function if every vertical line intersects the graph at most one point. Example: Find f + g, f - g, f·g, and f/g Operations on Functions: Homework: Page 53 check yourself 13 Homework: Page 53 check yourself 13
- 5. Composition of Functions Now let’s consider a very important way of combining two functions to get a new function. Given two functions f and g, the composite function f o g (also called the composition of f and g) is defined by (f o g)(x) = f( g(x) )
- 6. Example:
- 7. Inverse Functions Horizontal Line Test One-to-One Function A function f is one-to-one if and only if A function f with domain D and range R is a every horizontal line intersects the graph of f in at most one point. one-to-one function if either of the following equivalent conditions is satisfied: (1) Whenever a≠b in D, then f(a) ≠ f(b) in R. (2) Whenever f(a) = f(b) in R, then a=b in D. Example: Example: Check whether the following functions are one-to-one. f(x) = 3x + 1 g(x) = x2 - 3 h(x) = 1 - x
- 8. Inverse Function Let f be a one-to-one function with domain D and range R. A function g with domain R and range D is the inverse function of f, provided the following condition is true for every x in D and every y in R: y = f(x) The two graphs are reflections of each other through the line y = x , or are symmetric with respect to this line. if and only if x = g(y) How to find inverse of a function Solve the equation x = f(y) for y. f(x) = 3x + 7

No public clipboards found for this slide

×
### Save the most important slides with Clipping

Clipping is a handy way to collect and organize the most important slides from a presentation. You can keep your great finds in clipboards organized around topics.

Be the first to comment