Precalculus

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Rules of Thumb

All polynomials have the same amount of intercepts as their highest power (e.g. $x^3$ would have 3 intercepts). However, not all of these intercepts have to be real.

What to Review

General review of polynomial graphs like quadratics and cubics


Rational Functions

Of the form $f(x)=\frac{1}{x}$
Asymptotes
Vertical asymptotes: denominator of rational function cannot equal 0. If it does for any value of $x$, then the function becomes indeterminate at that point and there exists a vertical asymptote.
Horizontal asymptotes: 3 rules
If the degree of the numerator is less than the degree of the denominator, then the x-axis is the horizontal asymptote
If the degree of the numerator is equal to the degree of the denominator, then the ratio of leading coefficients is the horizontal asymptote
If the degree of the numerator is greater than the degree of the denominator, then there is no horizontal asymptote
Graphing
To graph rational functions, you only need to plot one point and determine where you need to reflect it to in order to complete the graph


Parametric Equations

Like an etch-a-sketch
A set of parametric equations is two or more functions governed by the same parameter, for example $t$:
$x=t^2, y=t^3-4t, -3\leq t\leq3$