## Search Results

### 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

Found in: Pre-Calculus
• #### 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

Found in: Pre-Calculus
• #### 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

• #### 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

• #### 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

• #### 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

Found in: Pre-Calculus
• #### 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 + . . .

Found in: Pre-Calculus
• #### 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.

• #### Pre-Calculus Unit Circle

In pre-calculus, 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

Found in: Calculus
• #### Right Triangles and Trig Functions for Pre-Calculus

If you’re studying pre-calculus, 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:

Found in: Calculus
• #### How to Format Interval Notation in Pre-Calculus

In pre-calculus 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.

Found in: Calculus
• #### Absolute Value Formulas for Pre-Calculus

Even though you’re involved with pre-calculus, you remember your old love, algebra, and that fact that absolute values then usually had two possible solutions. Now that you’re with pre-calculus, you realize

Found in: Calculus
• #### Trig Identities for Pre-Calculus

Of course you use trigonometry, commonly called trig, in pre-calculus. And you use trig identities as constants throughout an equation to help you solve problems. The always-true, never-changing trig identities

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 y-intercepts for a rational function, you have all the information you need to start graphing the function. Rational functions with equal degrees in

Found in: Functions
• #### Understanding the Properties of Numbers

Remembering the properties of numbers is important because you use them consistently in pre-calculus. The properties aren’t often used by name in pre-calculus, but you’re supposed to know when you need

• #### How to Graph Linear Inequalities

You can use the slope-intercept form to graph inequalities. The slope-intercept form is expressed as y = mx + b, where the variable m stands for the slope of the line, and

• #### How to Use a Graphing Calculator

It’s a good idea to purchase a graphing calculator for pre-calculus work. Since the invention of the graphing calculator, math classes have begun to change their scope. A graphing calculator does so many

• #### 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

• #### 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

• #### 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

• #### 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 y-axis, which changes its height. A number

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 x-axis. A number multiplying a variable inside a function affects the horizontal

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

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:

Found in: Functions
• #### How to Graph Functions with More than One Rule: Piece-wise Functions

Functions with more than one rule (called piece-wise functions) are broken into pieces, depending on the input. Although a piece-wise function has more than one function, each function is defined only

Found in: Functions

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