Sketch A Graph Of A Polynomial Function
Translating a function example.
Sketch a graph of a polynomial function. Find relative extrema of a function f x x 3 x. Predict the end behavior of the function. If the function is an even function its graph is symmetric with respect to the y axis that is f. Given a graph of a polynomial function of degree n identify the zeros and their multiplicities if the graph crosses the x axis and appears almost linear at the intercept it is a single zero.
To sketch any polynomial function you can start by finding the real zeros of the function and end behavior of the function. Plot the x and y intercepts on the coordinate plane. For example if you have found the zeros for the polynomial f x 2 x4 9 x3 21 x2 88 x 48 you can apply your results to graph the polynomial as follows. Use the end behavior and the behavior at the intercepts to sketch a graph.
As x x the function f x f x so we know the graph continues to decrease and we can stop drawing the graph in the fourth quadrant. Sketch the graph of polynomial p x x 3 2 x 2 24 x. If the graph touches the x axis and bounces off of the axis it is a zero with even multiplicity. Determine the end behavior by examining the leading term.
Using technology we can create the graph for the polynomial function shown in figure 16 and verify that the resulting graph looks like our sketch in figure 15. Scaling a function example. If a function is an odd function its graph is symmetrical about the origin that is f x f x. Steps involved in graphing polynomial functions.
Find the inflection points of x 4 x 2 4. Inverse of a function example. Once you have found the zeros for a polynomial you can follow a few simple steps to graph it. 4th order polynomial example.
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