Answered: Given a polynomial function f(x)= (x -…

Math

Calculus

Given a polynomial function f(x)= (x - 1)} (x +2)x – 3).

Trigonometry (MindTap Course List)

10th Edition

ISBN:9781337278461

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Complex Numbers

Section4.2: Complex Solutions Of Equations

Problem 7ECP: Find the cubic polynomial function f with real coefficients that has 1 and 2+i as zeros, and f2=2.

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Concept explainers

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.

Question

i) What is the degree of f ?
ii) Determine the zeros of f and their multiplicities.Also, determine whether the graph of f crosses or touches the x-axis at each zero.
iii) Determine its y-intercept.
iv) Determine the end behavior of f.
v) Sketch the graph of the polynomial function.Make sure your graph shows all intercepts and exhibits the proper end behaviour.

Given a polynomial function f(x)= (x – 1)°(x + 2)(x– 3).

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