Question

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

Answer 1

"Graph D" is the one among the following choices given in the question that represents 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.

Answer 2

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 is$f(x)\to+\infty$, 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 $f(x)\to+\infty$ as$x\to\infty$.) 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.