#11 a-c 327464Page <11. Let f(r) = x-3r2-4. Perform the following steps to finally graph the polyno-mial.a). How many zeros does f(r) have (including multiplicities)?b). List all the possible rational zeros using the Rational Zero Theorem.c). Use Synthetic Division (or Long Division) to check one by one, if the possiblezeros listed above is actually a real zero of the polynomial function f(x).

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Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section: Chapter Questions

Problem 1DE

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If the result of a polynomial division is 2x3 − 4x2 − 5x +23x + 2, make at least threedefinitive statements about the ???????? and the ??????? that is involved. Do you agree with the contention that the functions f(x) = x + 2 and g(x) =x2 − 4x − 2are the same in every respect. Provide evidence to support your position. Do you agree with the statement that “ cubic functions must have at least 1x-intercept but not more than 3, whereas quadratic functions may or may not have x-intercepts.Provide evidence to support your position.
Use the Intermediate Value Theorem to show there is a solution to x2 − 16 = 2 in the x2 − 9interval (1, 2).
Graph the rational function, and find all vertical asymptotes, x- and y-intercepts, and local extrema, correct to the nearest tenth. (If an answer does not exist, enter DNE.)y=(2x2-7x)/(2x+5) Local maximum?Local minimum?Use long division to find a polynomial that has the same end behavior as the rational function. g(x) = ?
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2. If a third degree polynomial has a lone x-intercept atx = a , discuss what this implies about thelinear and quadratic factors of that polynomial.
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If the rational function y  r1x2 has the horizontalasymptot
2. Use Rolle’s Theorem to prove that 5 − 3x − x3 does not have more than 1 root.
1. If the result of a polynomial division is 2x3 − 4x2 − 5x + 23 x + 2, make at least three definitive statements about the dividend and the divisor that is involved. 2. Do you agree with the contention that the functions f(x) = x + 2 and g(x) = x2 − 4 x − 2 are the same in every respect. Provide evidence to support your position. 3. Do you agree with the statement that “ cubic functions must have at least 1 x-intercept but not more than 3, whereas quadratic functions may or may not have x-intercepts. Provide evidence to support your position.

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