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Section 4.2 - to find the y intercept let x = 0 i.e f(0 is...

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Section 4.2 Graphing Polynomial Functions if P(x) is a polynomial function of degree n, the graph of the function has: at most n real zeros, and thus at most n x-intercepts; at most n - 1 turning points. Turning point are relative maxima and minima where the function changes from decreasing to increasing or from increasing to decreasing. To graph a polynomial function: 1. Use the leading term test to determine the end behavior. 2. Find the zeros of the function by solving f(x) = 0. Real zeros are x-intercepts of the graph. Plot these points. . Use the multiplicity of each zero to determine if the graph crosses or touches at each zero. 3. Choose x values in between each real zero. Find the corresponding y values to have a more points to plot. 4. Find and plot the y-intercept.
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Unformatted text preview: to find the y- intercept, let x = 0. i.e. f(0) is the y-intercept. 5. Find a plot more points if necessary to see the shape of the graph. 6. Check that there are the correct number of zeros and turning points and that the graph crosses and touches the x-axis where it should. Graph. h(x) = x 3-x Graph g(x) = -x 3 + 2x 2 + 4x -8 The Intermediate Value For any polynomial function P(x) with real coefficients, if a ≠ b and P(a) and P(b) are of opposite signs, then the function has a real zero between a and b. This means that the graph of the function either crosses or touches the x-axis between a and b. Use the intermediate value theorem to determine. if possible, whether the function f has a real zero between a and b. f(x) = 2x 5-7x + 1; a = 1, b = -2...
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