# MATH 2A Lecture Notes - Lecture 2: Algebraic Function, Cube Root, Logarithm

MATH 2A - Lecture 2 - Mathematical Models and DIfferent Types of Functions

A mathematical model is a mathematical description (often by means of function) or

(equations) of a real-world phenomenon.

● Examples:

○ Speed of a falling object

○ Population

○ Concentration of a product in a chemical reaction

○ Life expectancy of a person at birth

Linear Models

● The graph of the function is a line and it follows the

following format:

○ f(x|=mx+b

● In the example on the right,

○ Slope, m = 3

○ Intercept b = -2

*image from MCA online

Polynomial function

● A function f is called polynomial if:

○(x)x x x .. x xf =ann+an−1 n−1 +an−2 n−2 +. +a22+a1+ao

○ are called polynomial coefficients,a... aa0 1, n

○ If , n is the degree of polynomial=an/ 0

■ Leading coefficient

Example:

(x)x xf = 2 6−x4+5

23+ √2

Solution:

● The polynomial is of degree 6

● There are two famous types of polynomials

○ {f(x)=ax²+bx+c

○ {f(x)=ax³+bx²+cx+d

3-Power Function

## Document Summary

Math 2a - lecture 2 - mathematical models and different types of functions. A mathematical model is a mathematical description (often by means of function) or (equations) of a real-world phenomenon. Concentration of a product in a chemical reaction. Life expectancy of a person at birth. The graph of the function is a line and it follows the following format: A function f is called polynomial if: n 2 + . + a2 x n 1 + an 2 x n + an 1 x (x) x. = 2 6 x4 + 5 x. There are two famous types of polynomials. , where a is a constant is called a power function. Depending on the value of a we can have different shapes for power functions. = x (x) f: a = n and is a positive integer, a=1/n where n is a positive integer. Y = x y = 3 x root 3 or cube root: a=-1, y=1/x.