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179 results for "Yang Kuang, PhD"

How to Decompose Partial Fractions
A process called partial fractions takes one fraction and expresses it as the sum or difference of two other fractions. In calculus, this process is useful before you integrate a function. Because integration [more…]
Found in: PreCalculus 
How to Factor a Polynomial Expression
In mathematics, factorization or factoring is the breaking apart of a polynomial into a product of other smaller polynomials. If you choose, you could then multiply these factors together, and you should [more…]
Found in: PreCalculus 
How to Graph a Circle
The first thing you need to know in order to graph the equation of a circle is where on a plane the center is located. The equation of a circle appears as [more…]
Found in: Graphing Equations 
How to Graph an Ellipse
An ellipse is a set of points on a plane, creating an oval, curved shape, such that the sum of the distances from any point on the curve to two fixed points [more…]
Found in: Graphing Equations 
How to Graph a Hyperbola
Think of a hyperbola as a mix of two parabolas — each one a perfect mirror image of the other, each opening away from one another. The vertices of these parabolas are a given distance apart, and they open [more…]
Found in: Graphing Equations 
How to Solve Linear Systems
When you solve systems with two variables and therefore two equations, the equations can be linear or nonlinear. Linear systems are usually expressed in the form Ax + By [more…]
Found in: PreCalculus 
How to Solve Systems that Have More than Two Equations
Larger systems of linear equations involve more than two equations that go along with more than two variables. These larger systems can be written in the form Ax + By + Cz + . . . [more…]
Found in: PreCalculus 
How to Graph a Rational Function When the Numerator Has the Higher Degree
Rational functions where the numerator has the greater degree don’t actually have horizontal asymptotes. Instead, they have oblique asymptotes which you find by using long division. [more…]
Found in: Graphing Equations 
PreCalculus Unit Circle
In precalculus, the unit circle is sort of like unit streets, it’s the very small circle on a graph that encompasses the 0,0 coordinates. It has a radius of 1, hence the unit. The figure here shows all [more…]
Found in: Calculus 
Right Triangles and Trig Functions for PreCalculus
If you’re studying precalculus, you’re going to encounter triangles, and certainly the Pythagorean theorem. The theorem and how it applies to special right triangles are set out here: [more…]
Found in: Calculus 
How to Format Interval Notation in PreCalculus
In precalculus you deal with inequalities and you use interval notation to express the solution set to an inequality. The following formulas show how to format solution sets in interval notation. [more…]
Found in: Calculus 
Absolute Value Formulas for PreCalculus
Even though you’re involved with precalculus, you remember your old love, algebra, and that fact that absolute values then usually had two possible solutions. Now that you’re with precalculus, you realize [more…]
Found in: Calculus 
Trig Identities for PreCalculus
Of course you use trigonometry, commonly called trig, in precalculus. And you use trig identities as constants throughout an equation to help you solve problems. The alwaystrue, neverchanging trig identities [more…]
Found in: Calculus 
How to Graph a Rational Function with Numerator and Denominator of Equal Degrees
After you calculate all the asymptotes and the x and yintercepts for a rational function, you have all the information you need to start graphing the function. Rational functions with equal degrees in [more…]
Found in: Functions 
Understanding the Properties of Numbers
Remembering the properties of numbers is important because you use them consistently in precalculus. The properties aren’t often used by name in precalculus, but you’re supposed to know when you need [more…]
Found in: PreAlgebra & Algebra Basics 
How to Graph Linear Inequalities
You can use the slopeintercept form to graph inequalities. The slopeintercept form is expressed as y = mx + b, where the variable m stands for the slope of the line, and [more…]
Found in: PreAlgebra & Algebra Basics 
How to Use a Graphing Calculator
It’s a good idea to purchase a graphing calculator for precalculus work. Since the invention of the graphing calculator, math classes have begun to change their scope. A graphing calculator does so many [more…]
Found in: Graphing Equations 
Comparing Radicals and Exponents
Radicals and exponents (also known as roots and powers) are two common — and oftentimes frustrating — elements of basic algebra. And of course they follow you wherever you go in math, just like a cloud [more…]
Found in: PreAlgebra & Algebra Basics 
How to Rewrite Radicals as Exponents
When you’re given a problem in radical form, you may have an easier time if you rewrite it by using rational exponents— exponents that are fractions. You can rewrite every radical as an exponent by using [more…]
Found in: PreAlgebra & Algebra Basics 
How to Rationalize a Radical Out of a Denominator
A convention of mathematics is that you don’t leave radicals in the denominator of an expression when you write it in its final form. Thus we do something called [more…]
Found in: PreAlgebra & Algebra Basics 
How to Vertically Transform Parent Graphs
When you apply a vertical transformation to a parent graph, you are stretching or shrinking the graph along the yaxis, which changes its height. A number [more…]
Found in: Functions 
How to Horizontally Transform Parent Graphs
When you apply a horizontal transformation to a parent graph, you are stretching or shrinking the graph horizontally, along the xaxis. A number multiplying a variable inside a function affects the horizontal [more…]
Found in: Functions 
How to Translate a Function's Graph
When you move a graph horizontally or vertically, this is called a translation. In other words, every point on the parent graph is translated left, right, up, or down. Translation always involves either [more…]
Found in: Functions 
How to Reflect a Function's Graph
Reflections take a parent function and provide a mirror image of it over either a horizontal or vertical line. You’ll come across two types of reflections: [more…]
Found in: Functions 
How to Graph Functions with More than One Rule: Piecewise Functions
Functions with more than one rule (called piecewise functions) are broken into pieces, depending on the input. Although a piecewise function has more than one function, each function is defined only [more…]
Found in: Functions