Problem: Article: There are as many different graphing strategies out there as there are types of functions, far too many to completely cover here. If you're struggling, and estimations won't work, check out articles on:  Quadratic functions Rational functions Logarithmic functions  Graphing inequalities (not functions, but still useful information). . Zeros, also called x-intercepts, are the points where the graph crosses the horizontal line on the graph. While not all graphs even have zeros, most do, and it is the first step you should take to get everything on track. To find zeros, simply the entire function to zero and solve. For example:  F(x)=2x2−18{\displaystyle F(x)=2x^{2}-18}  Set F(x) equal to zero: 0=2x2−18{\displaystyle 0=2x^{2}-18}   Solve: 0=2x2−18{\displaystyle 0=2x^{2}-18}  18=2x2{\displaystyle 18=2x^{2}} 9=x2{\displaystyle 9=x^{2}}  x=3,−3{\displaystyle x=3,-3} This is usually points where the graph does not exist, like where you are dividing by zero. If your equation has a variable in a fraction, like y=14−x2{\displaystyle y={\frac {1}{4-x^{2}}}}, start by setting the bottom of the fraction to zero. Any places where it equals zero can be dotted off (in this example, a dotted line at x=2 and x=-2), since you cannot ever divided by zero. Fractions, however, are not the only places you can find asymptotes. Usually, all you need is some common sense:  Some squared functions, like F(n)=n2{\displaystyle F(n)=n^{2}} can never be negative. Thus there is an asymptote at 0. Unless you're working with imaginary numbers, you cannot have −1{\displaystyle {\sqrt {-1}}}  For equations with complex exponents, you may have many asymptotes. Simply pick a few values for x and solve the function. Then graph the points on your graph. The more complicated the graph, the more points you'll need. In general, -1, 0, and 1 are the easiest points to get, though you'll want 2-3 more on either side of zero to get a good graph.  For the equation y=5x2+6{\displaystyle y=5x^{2}+6}, you might plug in -1,0,1, -2, 2, -10, and 10. This gives you a nice range of numbers to compare. Be smart selecting numbers. In the example, you'll quickly realize that having a negative sign doesn't matter -- you can stop testing -10, for example, because it will be the same as 10. This gives you an idea of the general direction of a function, usually as a vertical asymptote. For example -- you know that eventually, y=x2{\displaystyle y=x^{2}} gets really, really big. Just one additional "x" (one million vs. one million and one) makes y much bigger. There are a few ways to test end behavior, including:  Plug in 2-4 large values of x, half negative and half positive, and plot the points. What happens if you plugged in "infinity" for one variable? Does the function get infinitely bigger or smaller? If the degrees are the same in a fraction, like F(x)=x3−2x3+4{\displaystyle F(x)={\frac {x^{3}}{-2x^{3}+4}}}, simply divide the first two coefficients (1−2{\displaystyle {\frac {1}{-2}}} to get your ending asymptote (-.5).  If the degrees are different in a fraction, you must divide the equation in the numerator by the equation in denominator by Polynomial Long Division. Once you have 5-6 points, asymptotes, and a general idea of end behavior, plug it all in to get an estimated version of the graph. Graphing calculators are powerful pocket computers that can give exact graphs for any equation. They allow you to search exact points, find slope lines, and visualize difficult equations with ease. Simply input the exact equation into the graphing section (usually a button labeled "F(x) = ") and hit graph to see your function at work.
Summary: Understand how to graph common equation types. Find any zeros first Find and mark any horizontal asymptotes, or places where it is impossible for the function to go, with a dotted line. Plug in and graph several points. Map the end behavior of the function to see what happens when it is really huge. Connect the dots, avoiding asymptotic and following the end behavior to graph an estimate of the function. Get perfect graphs using a graphing calculator.

In one sentence, describe what the following article is about: Anger proves that the person has gotten to you. It means that you take the other person seriously and perhaps that you believe there is truth to the insult. Getting emotional will also make it harder to think clearly and respond. Insults are often a away to establish social hierarchy. Taking offense will give the other person an edge over you in inter-group dynamics. If you laugh and make a self-deprecating joke, you demonstrate that the other person's insult did not affect you. This can disarm your assailant and prove that you don't consider them a credible threat to your social status.  If the person in question is someone you respect and the comment has an element of truth to it, consider whether the "insult" might have been constructive criticism. If so, try to follow the advice. This is generally preferable to returning the insult. Returning the insult means that you consider it a credible threat to your social status. It validates the insult and, unless you can execute a comeback very effectively, you will come out on bottom.  It was often alleged, for example, that Ronald Reagan was too old to serve as President. Instead of going on the counterattack, he diffused the situation with self-deprecating humor:  "Thomas Jefferson once said, 'One should not worry about chronological age compared to the ability to perform the task.' . . . Ever since he told me that I stopped worrying about my age." "The dozens" is a traditional African-American game in which two people trade witty retorts. Familiarize yourself with some effectively lines, so that you can return an insult quickly and naturally. Practice your delivery to get your timing down. This response is best reserved for friends who won't take offense.  To be effective the insult should sound creative. But the standard format of "Your mom is so ____" or "You are so ____"  is a good go to. Examples include: "Your mom is so generous she would give you the hair off her back" or "Your mom is so old she was the waitress at the last supper."
Summary:
Don't get angry. Consider accepting the insult. Play the dozens.