accurately graph the polynomial function in Exercises 1 and 2 by showing all 6 steps of the procedure for graphing polynomial function as shown below. Use a chart with properly labeled columns and rows for the intervals, test points, function values, signs, and location of points on the graph in Step 3. To Graph a Polynomial Function: End behavior. Use the Leading-Term Test to determine and sketch the end behavior. Zeros and x-intercepts. Solve P(x) = 0. Name the zeros of the function (and their multiplicities). Give the x-intercepts (a real number zero is the first coordinate of an x-intercept). Test Points. Use the zeros to divide the x-axis into intervals and choose a test point in each interval to determine the sign of all function values in that interval. Use a chart with properly labeled columns and rows for the intervals, test points, function value at each test point, and location of points on the graph (ordered pair) in this step. y-intercept. Evaluate P(0). Give the y-intercept of the function. Additional points. Find additional ordered pair to determine the overall shape of the graph. Note: These points should be different from any point already found in Steps 1-4. Graph. Plot the intercepts and points found in the previous steps. Sketch a smooth curve that passes through these points and exhibits the required end behavior. f(x) = x^4-4x^3+3x^2 g(x) = -x^3+2x^2+4x-8

10th Edition

ISBN:9781337282291

Author:Ron Larson

Publisher:Ron Larson

Chapter3: Polynomial Functions

Section3.2: Polynomial Functions Of Higher Degree

Problem 33E: Finding Real Zeros of a Polynomial Function In Exercises 33-48, (a) find all real zeros of the...

To Graph a Polynomial Function:

End behavior. Use the Leading-Term Test to determine and sketch the end behavior.
Zeros and x-intercepts. Solve P(x) = 0. Name the zeros of the function (and their multiplicities). Give the x-intercepts (a real number zero is the first coordinate of an x-intercept).
Test Points. Use the zeros to divide the x-axis into intervals and choose a test point in each interval to determine the sign of all function values in that interval. Use a chart with properly labeled columns and rows for the intervals, test points, function value at each test point, and location of points on the graph (ordered pair) in this step.
y-intercept. Evaluate P(0). Give the y-intercept of the function.
Additional points. Find additional ordered pair to determine the overall shape of the graph. Note: These points should be different from any point already found in Steps 1-4.
Graph. Plot the intercepts and points found in the previous steps. Sketch a smooth curve that passes through these points and exhibits the required end behavior.

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