For each polynomials, follow all the steps indicated below to graph them: (a) Find the x- and y-intercepts of f. (b) Determine whether the graph of f crosses.

Slides:

Advertisements

Similar presentations

Graphs of Polynomial Functions Digital Lesson. Copyright © by Houghton Mifflin Company, Inc. All rights reserved. 2 Polynomial Function A polynomial function.

Advertisements

Section 2.2 Polynomial Functions of Higher Degree

Graphs of Polynomial Functions Copyright © by Houghton Mifflin Company, Inc. All rights reserved. 2 Polynomial Function A polynomial function is a function.

Identifying Key Features of Linear and Exponential Graphs

Notes Over 4.3 Finding Intercepts Find the x-intercept of the graph of the equation. x-intercept y-intercept The x value when y is equal to 0. Place where.

The “zero” of a function is just the value at which a function touches the x-axis.

Section 3.2 Polynomial Functions and Their Graphs.

Analyzing Graphs of Polynomials Section 3.2. First a little review… Given the polynomial function of the form: If k is a zero, Zero: __________ Solution:

Polynomial Functions and Models

Sullivan PreCalculus Section 3.2 Polynomial Functions

Polynomial Functions and End Behavior

Chapter 3 Section 3.2 Polynomial Functions and Models.

By Noureen Villamar Melissa Motieram Elizabeth Stasiak Period B.

Solving Equations Graphical Transformations Piecewise Functions Polynomial Functions

X-intercept(s): y-intercept: Domain: Axis of Symmetry: Zero(s): Range: What are the Characteristics of Quadratic Functions?? MM2A3c. Investigate and explain.

Polynomial Functions and Their Graphs

Section 4.1 Polynomial Functions. A polynomial function is a function of the form a n, a n-1,…, a 1, a 0 are real numbers n is a nonnegative integer D:

2.3 Polynomial Functions & Their Graphs Objectives –Identify polynomial functions. –Recognize characteristics of graphs of polynomials. –Determine end.

Warm Up: Solve & Sketch the graph:. Graphing Polynomials & Finding a Polynomial Function.

Polynomial Functions Zeros and Graphing Section 2-2.

Exponential Functions MM3A2e Investigate characteristics: domain and range, asymptotes, zeros, intercepts, intervals of increase and decrease, rate of.

Precalculus Lesson 2.2 Polynomial Functions of Higher Degree.

Today in Pre-Calculus Go over homework Notes: (need calculator & book)

CHARACTERISTICS OF FUNCTIONS x-intercept and y-intercept Maximum and Minimum of a Function Odd and Even Functions End Behavior of Functions.

Polynomial Functions and Their Graphs

Graphing Polynomials. Step One: Determine End Behavior Using Lead Coefficient Test.

Essential Question: How do you sketch the graphs of polynomial functions? Students will write a summary of how to sketch a graph of a polynomial function.

Graphs of Polynomial Functions. Parent Graphs  Quadratic Cubic Important points: (0,0)(-1,-1),(0,0),(1,1)  QuarticQuintic  (0,0) (-1,-1),(0,0),(1,1)

Warm up The domain of a function is its a)y-values b) x-values c) intercepts  The range of a function is its a) y-values b) x-values c) intercepts.

Characteristics of Polynomials: Domain, Range, & Intercepts

Polynomial Functions Algebra III, Sec. 2.2 Objective

STEPS: x4 + 3x3 – 12x2 + 12x < 0 x(x – 2)2 (x + 3) < 0

Section 3.2 Polynomial Functions of Higher Degree.

Bell Ringer. Zeroes of Polynomials October 28, 2015.

Polynomials have the property that the sum, difference and product of polynomials always produce another polynomial. In this chapter we will be studying.

Sullivan Algebra and Trigonometry: Section 5.1 Polynomial Functions Objectives Identify Polynomials and Their Degree Graph Polynomial Functions Using Transformations.

5.2 Polynomials, Linear Factors, and Zeros P

Warm Up Are the following graphs even or odd? (Draw them on your paper) 2.What are the zeros for the given polynomial function and what is the multiplicity.

Graphing Polynomial Functions. Finding the End Behavior of a function Degree Leading Coefficient Graph Comparison End Behavior As x  – , Rise right.

Graphs of Polynomial Functions. Copyright © by Houghton Mifflin Company, Inc. All rights reserved. 2 A polynomial function is a function of the form where.

5.2 Polynomials, Linear Factors, and Zeros

Polynomial Functions: What is a polynomial function?

4.2 Polynomial Functions and Models. A polynomial function is a function of the form.

Chapter 4 Polynomial (Poly) & Rational Functions Copyright ©2013, 2009, 2006, 2005 Pearson Education, Inc.

Section 4.2 Graphing Polynomial Functions Copyright ©2013, 2009, 2006, 2001 Pearson Education, Inc.

UNIT 2, LESSON 7 POLYNOMIAL AND RATIONAL INEQUALITIES.

Polynomials Graphing and Solving. Standards MM3A1. Students will analyze graphs of polynomial functions of higher degree. a. Graph simple polynomial functions.

Lesson 2.2 Read: Pages Page 112: #1-9 (EOO), (EOO), (EOO)

Graphs of Polynomial Functions Digital Lesson. Copyright © by Houghton Mifflin Company, Inc. All rights reserved. 2 Polynomial Function A polynomial function.

Chapter 3 Section 3.4 Polynomial Functions: Graphs, Applications and Models.

Grudgeball! Unit 4 (Part 2) Test Review. Factor completely:

4.2 Polynomial Functions of Higher Degree Objective: Identify zeros and multiplicities, determine end behavior, sketch polynomials.

1.8: Interpreting Graphs and Functions Unit 1: September 4, 2014.

Analyzing Functions Putting the FUN in Function!.

2.2 Power Function w/ modeling 2.3 Polynomials of higher degree with modeling.

Graphs of Polynomial Functions A-REI.10 Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate.

Where am I now? Review for quiz 4.1.

Warmup 3-7(1) For 1-4 below, describe the end behavior of the function. -12x4 + 9x2 - 17x3 + 20x x4 + 38x5 + 29x2 - 12x3 Left: as x -,

Section 3.2 Polynomial Functions and Their Graphs

Polynomial Multiplicity

Polynomial Functions and Their Graphs

Lesson 5.8 Graphing Polynomials.

3.3 Polynomial Functions and Models

3.3 Polynomial Functions and Models

“Why so serious?”.

How many solutions does the equations have?

Polynomial Functions of Higher Degree

Homework Answers: Operations

Presentation transcript:

For each polynomials, follow all the steps indicated below to graph them: (a) Find the x- and y-intercepts of f. (b) Determine whether the graph of f crosses or touches the x-axis at each x-intercept. (c) Describe the ends behavior as x gets closer to -  and  (d) Find the intervals on which the graph of f is above or below the x-axis. then sketch each polynomial and then determine (e) where the graph is increasing/decreasing. (f) where the relative extrema (maximum or minimum) are located. 1. f(x) = x(x − 2)(x − 4) Graphs and Behavior of Polynomials Name;______

2.f(x) = (x − 2)(x + 4) 2 3. f(x) = x 2 (x − 2)(x + 2)

Challenge Problems: 1. Make up a polynomial that has the following characteristics: crosses the x-axis at -1 and 4, touches the x-axis at 0 and 2, and is above the x-axis between 0 and 2. Is this polynomial unique? Compare your polynomial with those of other students. 2. Make up a polynomial that has the following characteristics: degree 6; four real zeros, one of multiplicity 3; y-intercept 3; behaves like y = −5x 6 for large values of |x|. Is this polynomial unique? Compare your polynomial with those of other students. What terms will be the same as everyone else’s?