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Graphing Inequalities

Inequalities are easy to graph once you get the hang of it, but did you know that there are various kinds of inequalities ? These simple steps will show you how to graph cubic, rational, square root, linear, and quadratic functions.

In this example of a cubic function, you will start off by making a table. You must know what your rule is in order to solve and complete the table before graphing your points. In this case, the y= rule is y=x^3, so you would simply cube each point before graphing it and then draw your function.

OR inequalities are used whenever you are analyzing opposites sides of a graph.

OR inequalities show that you are looking at two opposing sides of a graph. Since this is a rational function, your rule is 1/x. When having this rule in your inequality, your function will be graph in the 1st and 3rd quadrants of your graph and will travel without touching the y-axis. As you see, in this particular problem, you are able to factor rather than using the quadratic formula. After factoring, always remember to SET THE NUMBERS EQUAL TO ZERO!!! (For notes on the numberline, refer to the Quick Notes.)

When graphing lines, always make a table, solve using the rule, then graph point

When graphing square roots, be sure to graph your points after making a table. The rule you must follow in this case would be finding the square root of the x-values. If the pattern continued, the x-value would be 49 and the y-value would be 7.

When graphing a linear function, refer to y=mx+b. Your x-value is your slope and the b-value represents your y-intercept. Once you solve the steps (as written above) you will find your slope value (y). In this case, our slope is 1(/1). This stands for the rise/run of your graph. This means, the next point of the graph will be seen as you go up a y-intercept and cross an x-intercept.

(Ignore the linear part.) When graphing this particular inequality you would use the quadratic formula after graphing the lines. Any time you have an x^2, and an x behind a number as well a plain interval, you will have a quadratic function. Once we reach step number 6, the signs are pointing the same direction. This is known as a compound inequality, where you are analyzing all possible x-intercepts between two points.