Warm-up!! 1/15/2019 Day 6

1/15/2019 Homework Questions???

Are you ready for the Skills Check?? 1/15/2019 Day 6 Are you ready for the Skills Check??

State the Domain and Range 1/15/2019 State the Domain and Range

Are these Functions? If no, WHY NOT?? 1/15/2019 Are these Functions? If no, WHY NOT?? Input Output -2 2 1 4 5 6 YES NO

f(-2) = (-2)2 – 2(-2) + 3 f(-2) = 4 + 4 + 3 f(-2) = 11 1/15/2019 Evaluating a function f(x) = x2 – 2x + 3 when x = -2 f(-2) = (-2)2 – 2(-2) + 3 f(-2) = 4 + 4 + 3 f(-2) = 11

1/15/2019 Day 6 Skills Check

GSE Algebra I UNIT QUESTION: How can we use real-world situations to construct and compare linear and exponential models and solve problems? Standard: MGSE.APR.1 – add and subtract polynomials. Today’s Question: How do we combine like terms?

Adding and Subtracting Polynomials

Naming Polynomials MONOMIALS: A. A monomial is B. Some examples of monomials are: a number, variable, or a product of numbers and variables. x -20 4y -3a5

A. A polynomial is the ________ or ___________ of monomials. POLYNOMIALS: A. A polynomial is the ________ or ___________ of monomials. monomial the sum B. An example of a polynomial in one variable, x, would be x3+6x2+12x+8 C. How many MONOMIALS are there in the above polynomial? 4

B. Example: Find the degree of the following polynomial: The _________exponent in the polynomial determines the DEGREE OF A POLYNOMIAL in one variable. largest A. Example: The degree of –7x + 9 – 4x2 is ____ because ___ is the largest exponent in the polynomial. 2 2 B. Example: Find the degree of the following polynomial: x4 + 6x3 + 7x5 + 12x 5

B. The coefficient of the first term is called the _______________. STANDARD FORM A. The terms of a polynomial are in STANDARD FORM if they are ordered from left to right in ______________ order; which means from the ____________ exponent to the smallest. decreasing largest B. The coefficient of the first term is called the _______________. C. To write a polynomial in Standard Form, ______________ the terms of the polynomial in ______________ order according to the ________________ of the variables. Lead coefficient arrange decreasing exponent

STANDARD FORM D. Example: Write 9 + x – 4x3 in standard form. – 4x3 + x + 9 E. Example: Write 3x2 – 2 + 4x – 5x3 in standard form. – 5x3 + 3x2 + 4x - 2

B. Their _________ of terms C. Look at the chart for an explanation. Some polynomials have SPECIAL NAMES that are determined by the following: A. Their _________ or B. Their _________ of terms C. Look at the chart for an explanation. degree number

Polynomial Name by # of Terms DEGREE Name by Degree 12 8x 4x2 + 3 5x3 + x2 3x2 – 4x + 6 Monomial 0 Constant 1 Monomial 1 Linear Binomial 2 Quadratic 2 Binomial 3 Cubic 3 Trinomial 2 Quadratic

Adding Polynomials We don’t need the parenthesis. Underline, circle, double underline… LIKE terms.

Subtracting Polynomials We need to distribute the negative.

Simplify the following expressions 1/15/2019 Simplify the following expressions 4(x – 3) + 2x – 7 -2(2x + 1) – 3(5x – 2) 3(x3 – 2x2 + 5x +1)

Evaluating Functions

Find the indicated values by using the graph. 1/15/2019 Find the indicated values by using the graph. 5 g(4) = ___ g(9) = ___ g(5) = ___ g(___) = 1 What are the values for g(______) = 3? 4 9 10 1 & 7

Find the indicated values by looking in the table. 1/15/2019 Find the indicated values by looking in the table. 15 x h(x) 3 2 7 4 11 6 15 h(6) = ___ h(2) = ___ h(___) = 3 h(___) = 11 h(1) = ___ h(3) = ___ h(___) = 13 7 4 5 9 5

1/15/2019 Practice WS