Steps to Graph Polynomial Functions

Steps to Graph Polynomial Functions - found in this step to...

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Steps To Graph Polynomial Functions 1. Make sure the function is arranged in the correct descending order of power. f ( x ) = a n x n + a n -1 x n -1 + . . . + a 1 x + a 0 , where the leading coefficient a n 0 2. Determine the far-left and far-right behavior of the function. n is even n is odd a n > 0 up to the far-left up to the far-right x y down to the far-left up to the far-right x y a n < 0 down to the far-left down to the far-right x y up to the far-left down to the far-right x y
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3. Find the y -intercept. a. To find f (0), substitute zero everywhere x appears in the polynomial function. ( Hint: You should just be left with the constant term of the function.) b. Write your y -intercept in the form (0, __ ) c. Plot this point. 4. Find any x -intercepts. a. Set the function equal to zero. b. Solve the resulting equation by factoring (or use the Rational Zero Test to find the real zeros). c. Write the x -intercepts in the form ( __ , 0) d. Plot these points. NOTE: You will need the factored form
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Unformatted text preview: found in this step to complete the rest of the steps. f ( x ) = ( x- a )( x + b )( x- c ). . . 5. Determine whether or not the graph passes through each x-intercept. For each factor ( x- c ) k of the function f : œ If k is even , the graph will intersect but not cross the x-axis at ( c , 0). œ If k is odd , the graph will cross the x-axis at ( c , 0). 6. Make a T-chart with more points. f Choose values for x that lie closely to the right and left of each x-intercept on the number line. f Substitute values for x into the factored form of the function, not the expanded form found in step 1. f Pay attention to signs when you are simplifying. x y 7. Sketch the graph. Your graph should be a smooth, continuous curve that contains at most ( n- 1) turning points . Do not include any sharp corners or unnecessary humps....
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