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Gennadij [26K]
2 years ago
15

Which of the following graphs represents the function f(x) = x4 - 2x3 - 3x2 + 4x + 1?

Mathematics
2 answers:
dem82 [27]2 years ago
5 0
"Graph D" is the one among the following choices given in the question that represents <span>the function f(x) = x4 - 2x3 - 3x2 + 4x + 1. The correct option among all the options that are given in the question is the fourth option or the last option. I hope that this is the answer that has actually come to your desired help.</span>
s2008m [1.1K]2 years ago
4 0

Answer: Graph D will be correct graph for the given function.

Explanation:

Given function f(x) = x^4-2x^3-3x^2+4x+1

Since it is a bi-quadratic equation thus it must have 4 roots and (0,1) is one of its point.

Moreover, the degree of the function is even thus the end behavior of the function isf(x)\to+\infty, as x\to-\infty and f(x)\to+\infty as x\to+\infty

In graph A, function has four root but it does not have the end behavior same as function f(x).( because in this graph f(x)\to-\infty, as x\to-\infty and f(x)\to-\infty, as x\to+\infty.) so, it can not be the graph of given function.

In graph B,  neither  it has four root nor it has the end behavior same as function f(x).(because in this graph f(x)\to+\infty as  x\to-\infty and f(x)\to-\infty as x\to+\infty.) so, it can not be the graph of given function.

In graph C, neither  it has four root nor it has the same end behavior as function f(x).(because in this graph f(x)\to-\infty as  x\to-\infty and f(x)\to+\infty asx\to\infty.) so, it also can not be the graph of given function.

In graph D it has four root as well as it has the same end behavior as the given function. Also it passes through the point (0,1).

Thus, graph D is the graph of given function.



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I need help with this. Thanks <br><br><br> I need to find the degree
scoundrel [369]

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_____

<em>Comment on using a calculator</em>

If you use the ATAN2( ) function of a graphing calculator or spreadsheet, it will give you the angle in the proper quadrant. If you use the arctangent function (tan⁻¹) of a typical scientific calculator, it will give you a 4th-quadrant angle when the ratio is negative. You must recognize that the desired 2nd-quadrant angle is 180° more than that.

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It may help you to consider looking at the "reference angle." In this geometry, it is the angle between the vector v and the -x axis. The coordinates tell you the lengths of the sides of the triangle vector v forms with the -x axis and a vertical line from that axis to the tip of the vector. Then the trig ratio you're interested in is ...

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