Jeopardy 100 Composite Functions 500 300 200 400 600 Combining Functions 700 100 Combining Functions 500 300 200 400 600 Inverse Functions and Relations.

Slides:

Advertisements

Similar presentations

2.3 Combinations of Functions Introductory MATHEMATICAL ANALYSIS For Business, Economics, and the Life and Social Sciences (12 th Edition) Copyright ©

Advertisements

COMPOSITE FUNCTIONS. The composite function: fg means… Apply the rule for g, then, apply the rule for f. So, if f(x) = x 2 and g(x) = 3x + 1 Then fg(2)

Composition of Functions

Discrete Structures Chapter 5 Relations and Functions

EOC Practice #14 SPI EOC Practice #14 Write and/or solve linear equations, inequalities, and compound inequalities including those containing.

Lesson 3-9: More On Functions Objective Students will: Find composite functions Evaluate composite functions for a given value.

Function Operations Add or subtract functions. 2.Multiply functions. Composite Functions Find the composition of two functions.

Algebra 2 Tri-B Review!. LogarithmsSolving Polynomials Compostion of Functions & Inverses Rational Expressions Miscellaneous

4.1 Composite and inverse functions

Warm-up Arithmetic Combinations (f+g)(x) = f(x) + g(x) (f-g)(x) = f(x) – g(x) (fg)(x) = f(x) ∙ g(x) (f/g)(x) = f(x) ; g(x) ≠0 g(x) The domain for these.

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.

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))

Chapter 7 Radical Equations.

Do Now Determine the open intervals over which the following function is increasing, decreasing, or constant. F(x) = | x + 1| + | x – 1| Determine whether.

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

Algebra 2 Trig A Final Review #1 Hyperbola  Center (0, 0)  a = 8, b = 7, c =  Vertices: (+8, 0)  Foci: (, 0)  Slopes of asymptotes: +7/8 Hyperbola.

Chapter 7 7.6: Function Operations. Function Operations.

1.3 New functions from old functions: Transformations.

5.1 Composite Functions Goals 1.Form f(g(x)) = (f  g) (x) 2.Show that 2 Composites are Equal.

Composite Functions. O Finding a composite function simply means plugging one function into another function. O The key thing to remember is which way.

Math on the Mind. Composition of Functions Unit 3 Lesson 7.

Warmup Alg 31 Jan Agenda Don't forget about resources on mrwaddell.net Section 6.4: Inverses of functions Using “Composition” to prove inverse Find.

6-1: Operations on Functions (Composition of Functions)

3.6 Solving Absolute Value Equations and Inequalities

Jeopardy 100 Quadratic Techniques Higher Order Polynomials Polynomial Functions Inverses 500.

Lesson 2-8: Operations of Functions

1. 2 Graphing Polynomials W- Substitutions Roots and Zeros Operations on Functions Inverse Functions

Jeopardy Math Review Evaluating a Function Examining f(x) Examining the Graph of f(x) Combining Functions Inverses

Function Composition Given f(x) = 2x + 2 and g(x) = 2, find f ºg(x). f ºg(x)=f(g(x)Start on the inside. f(g(x)) g(x) = 2, so replace it. f(g(x)) = f(2)

Review finding inverses and composite functions using square roots To find an inverse mathamaticaly there is one simple rule: Switch the x and y XY.

Jeopardy Q $100 Q $100 Q $100 Q $100 Q $100 Q $200 Q $200 Q $200

PreCalculus 3-R Unit 3 Functions and Graphs. Review Problems Evaluate the function f (x) = x 2 + 6x at f (8). f (8) = 112 Evaluate the function at f (6).

Do Now: Perform the indicated operation.

Composition of functions

Operations on Functions Day 1 – Add, Subtract, Multiply and Divide

LESSON 1-2 COMPOSITION OF FUNCTIONS

Quiz PowerPoint Review

Calculus Section 3.6 Use the Chain Rule to differentiate functions

Finding the Inverse of a Function Algebraically

Functions JEOPARDY.

5.4 Multiplying Polynomials.

Algebra II Unit 1 Test Review: Equations and Inequalities

5-Minute Check Lesson 1-2A

Composition of Functions 1.

Section 5.1 Composite Functions.

Jeopardy Hosted By Mrs. Carrigan.

Combinations of Functions:

2-6: Combinations of Functions

2.6 Operations on Functions

Combinations of Functions

MATH 1310 Section 3.6.

3.5 Operations on Functions

Functions Collection: notation, inverse, composite

Perform the indicated operation.

3.6 – The Chain Rule.

Find the derivative of the following function: {image} .

Jeopardy Final Jeopardy Solving Equations Solving Inequalities

Composition of Functions

MATH 1310 Section 3.6.

Determine if 2 Functions are Inverses by Compositions

Warm Up Determine the domain of f(g(x)). f(x) = g(x) =

Use Inverse Functions Notes 7.5 (Day 2).

Replace inside with “x” of other function

Product and Composition of Limits

2-6: Combinations of Functions

Operations on Functions

Evaluate x = 3; 2x + 6.

Composition of Functions

Presentation transcript:

Jeopardy 100 Composite Functions Combining Functions Combining Functions Inverse Functions and Relations Inverse Functions and Relations Composite Functions 700

Combining Functions- 100 Answer: (f + g)(x) = 2x + 1 NEXT QUESTION Given f(x) = x + 5 and g(x) = x – 4, find (f + g)(x)

Combining Functions- 200 Answer: (f – g)(x) = x + 4 NEXT QUESTION Given f(x) = 3x + 1 and g(x) = 2x – 3, find (f – g)(x)

Combining Functions Answer: (f g)(x) = 6x 2 – 7x – 3 NEXT QUESTION Given f(x) = 3x + 1 and g(x) = 2x – 3, find (f g)(x)

Combining Functions Given f(x) = x 2 and g(x) = 4 – x, find (f/g)(x) Answer: (f/g)(x) = x 2 / (4 – x) NEXT QUESTION

Combining Functions- 500 Answer: (f/g)(x) = (3x 3 ) / 5 NEXT QUESTION Given f(x) = 3x 2 and g(x) = 5/x, find (f/g)(x)

Combining Functions- 600 Answer: (f – g)(x) = 4x - 8 NEXT QUESTION Given f(x) = 8x - 3 and g(x) = 4x + 5, find (f - g)(x)

Combining Functions- 700 Answer: (f g)(x) = 32 x x - 15 NEXT QUESTION Given f(x) = 8x - 3 and g(x) = 4x + 5, find (f g)(x)

Trivia Answer: Candle in the Wind NEXT QUESTION What became the best selling single of all-time in 1997?

Classify Real numbers- 400 Answer: Commutative of addition NEXT QUESTION Name the property: 3 + y = y + 3

Classify Real numbers- 500 Answer: Additive ID NEXT QUESTION Name the property: = 5

Composite Functions- 100 Answer: f[g(1)] = 15 NEXT QUESTION Given f(x) = 3x and g(x) = x + 4, find f[g(1)]

Composite Functions- 200 Answer: g[h(-3)] = 12 NEXT QUESTION Given h(x) = x 2 – 1 and g(x) = x + 4, find g[h(-3)]

Composite Functions- 300 Answer: [f◦g◦h](1) = 12 NEXT QUESTION Given f(x) = 3x, g(x) = x + 4, and h(x) = x 2 – 1, Find [f◦g◦h](1)

Composite Functions- 400 Answer: g[h(x)] = 3x - 12 NEXT QUESTION Given g(x) = 3x and h(x) = x – 4, find g[h(x)]

Composite Functions Answer: h[g(x)] = 3x x + 13 NEXT QUESTION Given g(x) = x – 2 and h(x) = 3x 2 + 1, Find h[g(x)]

Composite Functions- 600 Answer: (f ◦ g)(9) = 6 NEXT QUESTION Given: f = {(-1, 2), (5, 6), (0, 9)}, g = {(6, 0), (2, -1), (9, 5)} Find (f ◦ g)(9)

Composite Functions- 700 Answer: (g ◦ f)(5) = 0 NEXT QUESTION Given: f = {(-1, 2), (5, 6), (0, 9)}, g = {(6, 0), (2, -1), (9, 5)} Find (g ◦ f)(5)

Absolute Value equations-300 Answer: No solution NEXT QUESTION

Absolute Value equations-400 Answer: x=8, -4 NEXT QUESTION

Absolute Value equations-500 Answer: x=16, -19 NEXT QUESTION

Inverses Answer: { (-7, -3), (-1, 0), (9, 5), (13, 7) } NEXT QUESTION Find the inverse of the relation: { (-3, -7), (0, -1), (5, 9), (7, 13) }

Inverses NEXT QUESTION Find the inverse of the following function: f(x) = (3/4)x

Inverses NEXT QUESTION Find the inverse of the following function: g(x) = x-7 8

Inverses Answer: NO NEXT QUESTION Determine if the following functions are inverses of each other: f(x) = 13x – 13 g(x) = x - 1

Inverses Answer: YES NEXT QUESTION Determine if the following functions are inverses of each other: f(x) = 2x – 8 g(x) = ½x + 4

Inverses NEXT QUESTION Answer: YES Determine if the following functions are inverses of each other: f(x) = 9 + (3/2)x g(x) = (2/3)x - 6

Inverses NEXT QUESTION Find the inverse of the following function: f(x) = 3x - 2

Compound Inequalities- 300 Answer: All Real Numbers NEXT QUESTION

Compound Inequalities- 400 Answer: No solution NEXT QUESTION

Compound Inequalities- 500 Answer: x -17 NEXT QUESTION

Daily Double