Composition OF Functions.

Slides:

Advertisements

Similar presentations

Operations with Functions.

Advertisements

Rational Functions Characteristics. What do you know about the polynomial f(x) = x + 1?

Section 7.3 Power Functions and Functions Operations.

Composite Functions. Objectives  Add, subtract, multiply, and divide functions.  Find compositions of one function with another function.

Composition is a binary operation like addition, subtraction, multiplication and division are binary operations. (meaning they operate on two elements)

A. What is the definition of Domain? B. What is the definition of Range? Your answers should be a complete sentence.

Functions Domain and range The domain of a function f(x) is the set of all possible x values. (the input values) The range of a function f(x) is the set.

SOLUTION EXAMPLE 4 Graph an equation in two variables Graph the equation y = – 2x – 1. STEP 1 Construct a table of values. x–2–1 012 y31 –3–5.

Composition of Functions. Definition of Composition of Functions The composition of the functions f and g are given by (f o g)(x) = f(g(x))

2 pt 3 pt 4 pt 5 pt 1 pt 2 pt 3 pt 4 pt 5 pt 1 pt 2 pt 3 pt 4 pt 5 pt 1 pt 2 pt 3 pt 4 pt 5 pt 1 pt 2 pt 3 pt 4 pt 5 pt 1 pt Functions Quadratics 1 Quadratics.

Wednesday, March 25 Today's Objectives

Unit 6 GA2 Test Review. Find the indicated real n th root ( s ) of a. a. n = 3, a = –216 b. n = 4, a = 81 SOLUTION b. Because n = 4 is even and a = 81.

Combinations of Functions

Jeopardy Growing Exponentially Welcome to the Function Fun with Functions Snoitcunf A special Function Let’s Change it Up

Chapter 7 7.6: Function Operations. Function Operations.

Activity 2.5 Inflated Balloons. Read page 224 and do problems 1 through 3 Do problem 4 in your groups Do problem 5 in your groups Do problem 6 in your.

Operations on Functions Lesson 3.5. Sums and Differences of Functions If f(x) = 3x + 7 and g(x) = x 2 – 5 then, h(x) = f(x) + g(x) = 3x (x 2 – 5)

Function Inverse Quick review. {(2, 3), (5, 0), (-2, 4), (3, 3)} Domain & Range = ? Inverse = ? D = {2, 5, -2, 3} R = {3, 0, 4}

FUNCTION OPERATIONS. Students seem to understand that the following: (f+g)(x) means add the f(x) and the g(x) functions together. (fg)(x) mean multiply.

2.1 “Relations & Functions” Relation: a set of ordered pairs. Function: a relation where the domain (“x” value) does NOT repeat. Domain: “x” values Range:

Copyright © 2015, 2008, 2011 Pearson Education, Inc. Section 5.1, Slide 1 Chapter 5 Logarithmic Functions.

EXAMPLE 1 Find a positive slope Let (x 1, y 1 ) = (–4, 2) = (x 2, y 2 ) = (2, 6). m = y 2 – y 1 x 2 – x 1 6 – 2 2 – (–4) = = = Simplify. Substitute.

More Quarter test review Section 4.1 Composite Functions.

Domain and Range Restriction Pt What are the different symbols that you use when writing domain and range restrictions? Write your answer in a.

Jeopardy Factoring Functions Laws of Exponents Polynomial Equations Q $100 Q $200 Q $300 Q $400 Q $100 Q $200 Q $300 Q $400 Final Jeopardy Q $500.

Ch 9 – Properties and Attributes of Functions 9.4 – Operations with Functions.

Review of 1.4 (Graphing) Compare the graph with.

Inverse functions: if f is one-to-one function with domain X and range Y and g is function with domain Y and range X then g is the inverse function of.

6.2 – Antidifferentiation by Substitution. Introduction Our antidifferentiation formulas don’t tell us how to evaluate integrals such as Our strategy.

A. The parent graph is translated up 0.5 units.

Input/Output tables.

Functions JEOPARDY.

Calculus section 1.1 – 1.4 Review algebraic concepts

Prerequisite Skills VOCABULARY CHECK 1

Basic Math Skills.

Warmup Let f(x) = x – 3 and g(x) = x2. What is (f ○ g)(1)?

Composition of Functions

Fun with Functions!.

Functions Review.

Domain and range.

Objective 1A f(x) = 2x + 3 What is the Range of the function

Please find your new assigned seat!

Answers (1,2,6,4) (1,3). Answers (1,2,6,4) (1,3)

Warm Up Simplify. Assume all variables are positive.

Mrs. Allouch JEOPARDY Unit 8.

Function notation.

Activity 2.8 Study Time.

2-6: Combinations of Functions

2.6 Operations on Functions

Intro to Functions College Algebra

Composition OF Functions.

Composition of Functions

Work out (if you can, simplify your answer) 8 6.

MATH 1310 Section 3.6.

3.5 Operations on Functions

Unit 2 Lesson 1 Function Definitions.

Warm Up Determine the domain of the function.

1.5 Combination of Functions

By the end of this lesson, you will know how to: Evaluate a function

MATH 1310 Section 3.6.

Determine if 2 Functions are Inverses by Compositions

Exponential Functions

Combinations of Functions

2-6: Combinations of Functions

f(x) g(x) x x (-8,5) (8,4) (8,3) (3,0) (-4,-1) (-7,-1) (3,-2) (0,-3)

Do Now: Given f(x) = 2x + 8 and g(x) = 3x2 – 1 find the following.

Composition of Functions By: Dr. Julia Arnold.

Presentation transcript:

Composition OF Functions

Definition of composite functions Suppose f and g are functions such that the range of g is the subset of the domain of f. Then the composite function can be described by the equation

Let’s do an example together. • Substitute 2x-3 in for g(x): • Substitute into f(x): Next

Simplify:

• Substitute for g(x): • Substitute f(x) into g(x): • Simplify:

Another example Next

Try these on your own:

Answers:

Now we will go over how to find a value of composite of functions. Find each value. Substitute in g(x). Substitute into g(x). Simplify Next

Substitute into f(x). Simplify

Now you find the values using the same directions as in the last examples. Answer: 64 Answer: -5