How to Graph a Rational Function When the Numerator and Denominator Have Equal Degrees
Rational functions with equal degrees in the numerator and denominator behave the way that they do because of limits. What you need to remember is that the horizontal asymptote is the quotient of the leading [more…]
How to Identify the Four Conic Sections
When you slice up a cone, each conic section has its own standard form of an equation with x and y variables that you can graph on the coordinate plane. You can write the equation of a conic section if [more…]
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…]
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…]
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…]
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…]
How to Graph Polynomials
Finding the zeros is very important to graphing a polynomial, because they give you a general template for what your graph should look like. Remember that zeros are [more…]
How to Graph a Parabola
In order to graph a parabola correctly, it is important to note whether it is a horizontal or a vertical parabola. This is because while the variables and constants in the equations for both curves serve [more…]
Distinguishing among Linear, Separable, and Exact Differential Equations
You can distinguish among linear, separable, and exact differential equations if you know what to look for. Keep in mind that you may need to reshuffle an equation to identify it. [more…]
How to Graph Parent Functions
There are a handful of common families of functions that you see over and over again in many areas of mathematics. Some of the most common are quadratic and square root functions, cubic and cube root functions [more…]
How to Graph a Rational Function When the Denominator Has the Higher Degree
In any rational function where the denominator has a greater degree as values of x get infinitely large, the fraction gets infinitely smaller until it approaches zero [more…]
