CA_GPS_34 - x-axis[Hint pick a point between the zeros Step 6 Plot the points and connect them with a smooth and continuous curve r is called

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Rev. S08 http://faculty.valenciacc.edu/ashaw/ COLLEGE ALGEBRA NAME: ________________________________ GPS # 34 4.1 POLYNOMIAL FUNCTIONS II Class Time: ____________ Date: __________ Useful Guidelines: To Graph a Polynomial function, 0 1 1 1 ... ) ( a x a x a x a x f n n n n + + + + = ! ! , 0 ! n a * Step 1: Find the x -intercepts, if any (by solving the equation 0 ) ( = x f ), and the y -intercepts, ) 0 ( f . * Step 2: Determine whether the graph crosses (when r is a zero of odd multiplicity) or touches (when r is a zero of even multiplicity) the x -axis at each x -intercepts. * Step 3: Check the end behavior: For large x , the graph of f behaves like the graph of n n x a x f = ) ( . * Step 4: Determine the degree of f = n and the maximum number of turning points on the graph of f = n -1 . * Step 5: Use the x -intercept(s) to find the intervals on which f is above the x -axis and the intervals on which f is above the
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Unformatted text preview: x-axis. [Hint: pick a point between the zeros.] * Step 6: Plot the points and connect them with a smooth and continuous curve. . [ r is called a (real) zero of f , or root of f when ) ( = r f ] ) 2 ( ) 2 )( 4 ( ) ( 2 ! + ! = x x x x f (a) Find the x-intercepts and the y-intercepts of the above polynomial function f . (b) Determine whether the graph touches or crosses the x-axis at each x-intercept. (c) Check end behavior: Find the power function that the graph of f resembles for large values of x . (d) Determine the maximum number of turning points of the graph of f. (e) Use the x-intercept(s) to find the intervals on which the graph of f is above and below the x-axis. (f) Plot the points and connect them with a smooth and continuous curve....
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This note was uploaded on 10/18/2011 for the course MAC 1105 taught by Professor Russel during the Summer '07 term at Valencia.

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