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## Math 1.1 and 1.2 notes

1 review
by: Rukeem Collins

62

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# Math 1.1 and 1.2 notes MATH 1101

Marketplace > Georgia State University > Geography > MATH 1101 > Math 1 1 and 1 2 notes
Rukeem Collins
GSU

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these notes contain all the subject matter of section 1.1, and half the subject matter of 1.2
COURSE
INTRO TO MATHEMATICAL MODELING
PROF.
Changyong Zhong
TYPE
Class Notes
PAGES
4
WORDS
CONCEPTS
Math, functions
KARMA
Free

## 1

1 review
"Yes please! Looking forward to the next set!"
Ms. Aaliyah Crist

## Popular in Geography

This 4 page Class Notes was uploaded by Rukeem Collins on Tuesday January 19, 2016. The Class Notes belongs to MATH 1101 at Georgia State University taught by Changyong Zhong in Winter 2016. Since its upload, it has received 62 views. For similar materials see INTRO TO MATHEMATICAL MODELING in Geography at Georgia State University.

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## Reviews for Math 1.1 and 1.2 notes

Yes please! Looking forward to the next set!

-Ms. Aaliyah Crist

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Date Created: 01/19/16
1/14 .polynomials- an algebraic expression containing a finite number of addition, subtraction, and multiplication of constants and non-negative integer power. A polynomial can’t have negative powers of variables, fraction power of variables, variables in a denominator, or variables in a radicle. Ex: 5x-2y General form of a polynomial in x An x X+An-1 Leading term: the term with the highest power. The coefficient of the leading term is the leading coefficient. The highest degree is the degree. . Removing parenthesis a(b+c) Ab+ac. . Foil (front x front outer x outer inside x inside last x last) (A+b).(c+d)= ac+ad+bc+bd foiling is a way of simplifying two functions. . 1.1 Functions Two sets can have correspondence. Each element in the set corresponds with at least one element in the other set. 1 to 1 correspondence- each element corresponds uniquely to an element on the other set. Function- a correspondence such that there is only one response. This means that for every input, there is only one output. An output can have two inputs, though It is not a function if it has more than one correspondence between sets. Common notation y=f(x) (F of x) also known as function notation X=independent variable (input) Y=dependent variable (outcome) Can be shown in a table X |-1|0|1 | Y |1|2|3 | A graph(see in figure 1) And in a formula Y=x+2 Domain: all possible x values Range: all potential y values 1/19 .Function rules: The denominator cannot equal 0 The expression under a square root (radicand) has to be greater than or equal to 0. .Evaluate a function You put a variable into the function to get your y value. Figure 1 7 6 5 4 3 2 1 0 2 3 4 Vertical line test: a relationship is a function if the graph can’t be intersected by a vertical line more than ounce. How to find domain: check to see if x follows function rules. If there is no fractions or radicands, domain is all real numbers. If there is, then see function rules Interval notation- use interval notation to display possible domain values. Ex: (-∞,∞) [-2,∞) use parenthesis ( ( ) if you can equal the number, and a bracket (]) if you cannot equal the number. For the number Infinity, for example, you’d use a bracket. In equations with multiple domain conditions, both conditions have to be satisfied. Ex: X≠0 X≥-5 .Determining if a relationship is a function. Vertical line test: (see above) The output can’t have an even exponent. .finding function expression Ex: 3X+2Y=5 solve for Y and you get 3x-5/2 Graphing functions: find the corresponding y values for x Ex: Y= X+1 X|-2|-1|0|1|2 Y|-1|0|1|2|3 And put their corresponding X and Y values on a graph. Chart Title 5 4 3 2 1 0 -2 -1 0 1 2 3 -1 -2 .How to find intercepts For the x intercept, let Y=0, solve for X For Y intercept, let x=0, solve for Y Ex: Y=2X+ 4 subtract four, then divide by the coefficient -4/2, and you get X=-2. 1.2 .Linear functions are functions that can be written in the form Y=mx+b. it increases at a steady rate. In 3x+ 5 M=3 B=5 The domain is all real numbers The range is all real numbers Y intercept is Mx0+B X intercept is 0=MX+b Linear functions always have straight lines. If a line on a graph slopes up, m is positive, if it slopes down, it is negative, and it is straight, M is 0. If the line is vertical, it is not a function.

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