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Graphing-Functions

Graphing-Functions - Graphing Functions Basics Graphing...

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From MathMotivation.com – Permission Granted For Use and Modification For Non-Profit Purposes Graphing Functions Basics Graphing Functions By Including Intercepts A simple method of graphing only involves plotting points, chosen in more or less random manner. An improvement to this method involves plotting all intercepts first, and then plotting some additional points. Intercepts Method For Graphing Functions 1. Find and plot all intercepts . To find y-intercepts, let x=0 and solve for y. To find x-intercepts, let y=0 and solve for x. 2. Plot points on each side of each x-intercept . Find and plot at least one point between each two x-intercepts and one point on each side of the largest and smallest x-intercept. 3. Draw a smooth curve through the points from left to right. Example: Graph f(x) = x 3 – x. First, rewrite as y = x 3 – x. Now, find intercepts. When x = 0, we get y = 0 3 – 0 = 0. So our y-intercept is (0,0) When y=0, we get 0 = x 3 – x. We solve this equation. CONTINUED ON NEXT PAGE 0 = x 3 – x Given 0 = x(x 2 – 1) Use Distributive Property to factor out x. 0 = x(x + 1)(x – 1) Use Distributive Property to factor x 2 – 1. x = 0 The Zero Product Law allows us to let each factor = 0 x + 1 = 0 x – 1 = 0 x = -1 , x = 1 , x = 0 Solve each equation using Addition Property of Equality So the x-intercepts are ( -1 ,0), ( 1 ,0), and ( 0 ,0) We plot these points to get Now, find and plot points on each side of each of these x-intercepts by letting x= -2, x=-1/2, x=1/2, and x=2. Draw a smooth curve through the points.

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