MAT 111 - College Algebra Section 2.2: Functions Functions are special kinds of relations. A function is an assignment from a set A to a set B such that: 1. Every element in set A is assigned an element in B. 2. No element in A is assigned to more than on
MAT 111 - College Algebra Section 3.4 Zeros of Polynomial Functions An nth degree polynomial can have at most n real zeros. Examples 1. f (x) = x2 1
2. g (x) = (x 1)2
3. h(x) = x3 1
Above statement can be improved: An nth degree polynomial has precisely n
MAT 111 - College Algebra Section 3.3 Polynomial Division Objectives: 1. Learn how to divide a polynomial by another polynomial. 2. Learn the Remainder theorem. 3. Learn the Factor theorem. 1. There are two ways to divide a polynomial by another polynomia
MAT 111 - College Algebra Section 3.2 Polynomial Functions of Higher Degree Graphs of polynomial functions are: 1. Continuous. 2. Smooth.
Power functions are functions of the form f (x) = axn where n 0 is a non-negative integer and a = 0.
To sketch the gr
MAT 111 - College Algebra Chapter 3 Polynomial Functions A polynomial function is a function of the form f (x) = an xn + an-1 xn-1 + . . . + a1 x + a0 where n is a nonnegative integer, an = 0 and ai R for 0 i n. n is called the degree of the polynomial. I
MAT 111 - College Algebra Section 2.7: Inverse Functions Consider the function f (x) = cfw_(1, a), (2, b), (3, e) Df : Rf : Notice that for every x in the domain of f there exists a unique value y in the range of f . Moreover, associated with every y in t
MAT 111 - College Algebra Section 2.6: Combinations of Functions Objectives: 1. Learn how to add, subtract, multiply and divide functions. 2. Learn how to nd domain of the new functions formed by the above operations. 3. Learn how to compose functions and
MAT 111 - College Algebra Section 2.5: Shifting, Reecting and Stretching Graphs Objectives: 1. Know how to graph new functions from old using above transformations. 2. To write formulas of functions given their graphs by realizing the above transformation
MAT 111 - College Algebra Section 2.3: Analyzing Graphs of Functions Objectives: 1. Learn what a graph of a function is and how to graph a function. 2. Find domain and range of a function graphically. 3. Learn what zeros of a function are and how to nd th
MAT 111 - College Algebra Chapter 2 Functions and Their Graphs Section 2.1: Linear Equations in Two Variables Linear equations in two variables may have one of the following forms: 1. Slope-intercept form. 2. Two-point form. 3. Point-slope form. 4. Genera
MAT 111 - College Algebra Section 1.8 - Other Types of Inequalities
1. Polynomial Inequalities Algorithm to solving polynomial inequalities: (a) Make one side of the inequality equal to zero. (b) Determine the critical numbers (values that make the polyno
MAT 111 - College Algebra Section 1.7 - Linear Inequalities in One Variable
An inequality is an expression that involves the symbol(s) <, >, or . A solution set of an inequality is the set of all real numbers that are solutions to the inequality. That is,
MAT 111 - College Algebra Section 1.5 - Complex Numbers A complex number in standard form is a + bi . Two complex numbers a + bi and c + di are equal if and only if a = c and b = d.
Operations with complex numbers: 1. Addition: (a + bi) + (c + di) = (a +
MAT 111 - College Algebra Section 1.4 Quadratic Equations
General form of a quadratic equation is ax2 + bx + c = 0 where a, b and c are real numbers such that a = 0. How to solve quadratic equations: 1. Factoring Examples: solve the following (a) x2 - 6x
MAT 111 - College Algebra Section 1.3 - Examples 1. Write an algebraic expression for the verbal description: (a) The product of two consecutive natural numbers.
(b) The sum of the square of two consecutive even integers the rst of which is 2n.