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Operations with Functions and Polynomials 1-3 and 1-4

Operations with Functions and Polynomials 1-3 and 1-4. Unit 1 English Casbarro. Operations with Functions. You really already know how to do this. Recall, Combining Like Terms. Ex. 4x 4 - 5x 2 + 6 – 7x 4 + 10x 2 -13.

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Operations with Functions and Polynomials 1-3 and 1-4

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  1. Operations with Functions and Polynomials1-3 and 1-4 Unit 1 English Casbarro

  2. Operations with Functions You really already know how to do this. Recall, Combining Like Terms. Ex. 4x4- 5x2 + 6 – 7x4+ 10x2 -13. You would combine: 4x4 -7x4 - 5x2 + 10x2 + 6 -13 = -3x4 + 5x2 - 7

  3. Graphic Organizer-Function Notation Fill in the following table.

  4. Warm-up: Function Notation Given f(x) = 2x2 – 8 , g(x) = x2 + 5x + 6, and h(x) = 2x + 4, find each function and define the domain. 1. (f + g)(x) 2. (f – g)(x) 3. (g + h)(x) 4. (g – h)(x) 5. f(x) + h(x) 6. (fh)(x) 7. 8.

  5. 1-4: Polynomials Definitions A monomial is a number, a variable, or a product of both A polynomial is a monomial or a sum or difference of monomials. Each monomial in a polynomial is a term. The degree of a monomial is the sum of the exponents of the variables. The degree of a polynomial is the highest degree of all of the terms of the polynomial. The leading coefficient is the coefficient of the term with the highest degree. A polynomial function is a function whose rule is a polynomial. Identifying Polynomials:

  6. Identifying Polynomials Polynomials:3x4 2z 12 + 9z3½a7 0.15x101 3t2 – t 3 Not Polynomials: 3x |2b3 – 6b|m0.75 – m

  7. Ex. 1Identifying the degree of a Monomial Identify the degree of each monomial. A. x4B.12 C. 4a2bD. x 3y 4z You Try: Identify the degree of each monomial. 1a.x 3 1b. 7 1c. 5x 3y 21d.a 6bc 2

  8. Standard Form of a Polynomial

  9. Classifying by number of terms and by degrees.

  10. Turn in the following problems: • Business The manager of a gift-basket business will ship the • baskets anywhere in the country. The cost to mail a basket • based on its weight, x, in pounds is given by • C(x) = 0.03x 3 – 0.75x2 + 4.5x + 7. • a. What is the cost of shipping a 7-pound gift basket? • b.What is the cost of shipping a 19-pound gift basket? • 2. Reasoning The total number of lights in a triangular lighting rig • is related to the triangular numbers, as shown below. The nth • triangular number is given by . • a.Write a polynomial function that represents the (n + 1)th • triangular number, T(n + 1). • b.The difference between two consecutive triangular numbers is • T(n + 1) – T(n). Subtract these two polynomial functions and state a • conclusion about the difference between consecutive triangular numbers.

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