Category Archives: College Algebra

MAT 101 Online Lecture Notes: 3.2 Graphing Polynomial Functions

Polynomial functions have the following important property: “Every polynomial function of degree $n$ has at most $n$ real zeros.” This property is called the Fundamental Theorem of Algebra. As an application of this property, we see that a polynomial function … Continue reading

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MAT 101 Online Lecture Notes: 3.1 Polynomial Functions and Models

A polynomial is a function of the form $$P(x)=a_nx^n+a_{n-1}x^{n-1}+\cdots+a_1x+a_0.$$ The number $n$ is called the degree of the polynomial $P(x)$. The term $a_nx^n$ is called the leading term and $a_n$ is called the leading coefficient. The number $a_0$ is called … Continue reading

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MAT 101 Online Lecture Notes: 2.6 Solving Linear Inequalities

Linear Inequalities: Solving linear inequalities is as easy as solving linear equations. You only need to know the following principles. For a given inequality, Adding the same number to each side of the inequality does not change the symbol $<$. … Continue reading

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MAT 101 Online Lecture Notes: 2.5 More Equation Solving

Rational Equations: The Recipe of Solving Rational Equations First find the LCD (Least Common Denominator), i.e. the Least Common Multiple of all denominators. Multiply your rational equation by the LCD. Solve the resulting equation (usually a linear equation or a … Continue reading

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MAT 101 Online Lecture Notes: 2.4 Analyzing Graphs of Quadratic Functions

There are two important topics in this section: graphing the quadratic function $f(x)=ax^2+bx+c$ and finding the (absolute) maximum or the minimum value of $f(x)=ax^2+bx+c$. First the sign of the leading coefficient $a$ tells us some information about the graph. If … Continue reading

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MAT 101 Online Lecture Notes: 2.3 Quadratic Equations, Functions and Models

Main topic in this section is solving a quadratic equation $ax^2+bx+c=0$. There are three ways to solve a quadratic equation. The first one is 1. By Factoring: This is a typical method to solve a quadratic equation whenever the polynomial … Continue reading

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MAT 101 Online Lecture Notes: 1.7 Symmetry and Transformations II

In this notes, we study the remaining transformations of a function, namely horizontal shifting, vertical shifting, and dilation (stretching and shrinking). We also discuss how those transformations can be used to sketch the graph of a complicated function from its … Continue reading

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MAT 101 Online Lecture Notes: 1.7 Symmetry and Transformations I

Transformations of the graph of a function $y=f(x)$: The transformations we consider include reflection, horizontal shifting, vertical shifting, stretching and shrinking. Here we discuss reflection and related symmetries. In the following notes, we will discuss the rest of transformations. Reflection … Continue reading

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