Functions 2 2 1 3 Domain Range 1 0 3 2 5 xf(x) 7.

Slides:



Advertisements
Similar presentations
Graphs of Inverse Functions. Inverse Sine Function The horizontal line test shows that the sine function is not one-to-one and has no inverse function.
Advertisements

Graphs of Exponential and Logarithmic Functions
Inverse Functions Section 1.8.
Operations on Functions Composite Function:Combining a function within another function. Written as follows: Operations Notation: Sum: Difference: Product:
4.1 Inverses Mon March 23 Do Now Solve for Y 1) 2)
One-to One Functions Inverse Functions
Transformations xf(x) Domain: Range:. Transformations Vertical Shifts (or Slides) moves the graph of f(x) up k units. (add k to all of the y-values) moves.
Functions Definition A function from a set S to a set T is a rule that assigns to each element of S a unique element of T. We write f : S → T. Let S =
Objectives Determine whether the inverse of a function is a function.
Today in Pre-Calculus Go over homework questions Notes: Inverse functions Homework.
Objective: Students will be able to graph and transform radical functions.
Lesson 2.6 Read: Pages Page 152: #1-37 (EOO), 47, 49, 51.
Ch 4 - Logarithmic and Exponential Functions - Overview
Q Exponential functions f (x) = a x are one-to-one functions. Q (from section 3.7) This means they each have an inverse function. Q We denote the inverse.
What is the symmetry? f(x)= x 3 –x.
Aim: Review functions and their graphs Do Now: 1. Which graph are functions? 2. Write the equations
Topic 4: Functions 4.1 TLW identify functions and their domain and codomain.
CHAPTER 6 SECTION 6 : FUNCTIONS AND THEIR INVERSES.
Math 71B 9.2 – Composite and Inverse Functions 1.
Graphs of Functions The graph of a function gives you a visual representation of its rule. A set of points generated like we did in the previous section.
OBJECTIVES: Evaluate the inverse trigonometric functions Evaluate the compositions of trigonometric functions.
Math – Graphs of Functions 1. Graph of a function: the graph of all the function’s ordered pairs 2.
Inverse Functions.
4.1 – ONE-TO-ONE FUNCTIONS; INVERSE FUNCTIONS Target Goals: 1.Obtain the graph of the inverse function 2.Determine the inverse of a function.
1.8 Inverse Functions, page 222
Inverse Functions.
Math 71B 9.3 – Logarithmic Functions 1. One-to-one functions have inverses. Let’s define the inverse of the exponential function. 2.
are said to be if and only if and At the same time.
Chapter 3: Functions and Graphs 3.6: Inverse Functions Essential Question: How do we algebraically determine the inverse of a function.
1 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 9-1 Exponential and Logarithmic Functions Chapter 9.
Chapter 7 – Radical Equations and Inequalities 7.2 – Inverse Functions and Relations.
Section 5.1 The Natural Logarithmic Function: Differentiation.
Function A FUNCTION is a mathematical “rule” that for each “input” (x-value) there is one and only one “output” (y – value). Set of Ordered Pairs: (input,
5.2 Relations and Functions. Identifying Relations and Functions Relation: A set of ordered pairs. You can list the set of ordered pairs in a relation.
6.2 Inverse functions and Relations 1. 2 Recall that a relation is a set of ordered pairs. The inverse relation is the set of ordered pairs obtained by.
Math – Exponential Functions
OBJECTIVES:  Find inverse functions and verify that two functions are inverse functions of each other.  Use graphs of functions to determine whether.
Notes Over 9.2 Graphing a Rational Function The graph of a has the following characteristics. Horizontal asymptotes: center: Then plot 2 points to the.
Ch 9 – Properties and Attributes of Functions 9.5 – Functions and their Inverses.
Inverse Functions Objective: To find and identify inverse functions.
Do Now: Given f(x) = 2x + 8 and g(x) = 3x 2 – 1 find the following. 1.) (f + g)(x) 2.) g(x – 2)
5.3 Inverse Functions (Part I). Objectives Verify that one function is the inverse function of another function. Determine whether a function has an inverse.
Objectives: 1)Students will be able to find the inverse of a function or relation. 2)Students will be able to determine whether two functions or relations.
One-to-One Functions A function is one-to-one if no two elements of A have the same image, or f(x1)  f(x2) when x1  x2. Or, if f(x1) = f(x2), then.
Functions 4 Reciprocal & Rational Functions
3.1 Functions x is called the independent variable
Warm Up Solve for x in terms of y
Relations and Functions
4-5:One-to-One Functions and Their Inverses
Lesson 1.6 Inverse Functions
5.3: Function Rules, Tables, and Graphs
The Inverse Sine, Cosine, and Tangent Functions
1.7 Represent Graphs as Functions
VERTICAL LINE TEST GRAPHS can represent functions.
Inverse Functions
Inverse Functions.
Ch 1.6: Inverse of Functions and Relations
5.3: Function Rules, Tables, and Graphs
{(1, 1), (2, 4), (3, 9), (4, 16)} one-to-one
Sec. 2.7 Inverse Functions.
7.4 Slope Objectives: To count slope To use slope formula.
3.6 - Inverse Functions Notation: Say: “f-inverse of x”…
Section 4.1: Inverses If the functions f and g satisfy two conditions:
Composite Function: Combining a function within another function.
Packet #12 Composite, One-to-one, and Inverse Functions
Packet #13 Exponential and Logarithmic Functions Math 160 Packet #13 Exponential and Logarithmic Functions.
Exponential Functions and Their Graphs
Functions What is a function? What are the different ways to represent a function?
Do Now: Given f(x) = 2x + 8 and g(x) = 3x2 – 1 find the following.
Chapter 4 Review What quadrant is point (-3, 2) in?
Presentation transcript:

Functions Domain Range xf(x) 7

Functions 2 3 NB Rule of thumb: “Vertical Ruler”: ANY vertical line drawn through the graph cuts it only once gives a function. And “Horizontal Ruler”: ANY HORIZONTAL line drawn AS WELL cuts graph only once, gives this special-case:- a one-to-one function. Identify common functions or classes of functions and test for 1 – 1 property.

Functions 2 4 f Inverse Functions

Functions 3 5 So … and vice versa You know already.. As composite functions:- )

Functions 3 6

7

8

9

Functions 2 10 Do:- Bk 11, Page 62 Ex 3.3