Question

Which of the graphs below represent the function f(x) = − x3 + 4x2 − x + 3? You may sketch the graph to compare.

Answer 1

Answer:

Please see the attachment.

Step-by-step explanation:

$\text{Given function:}f(x)=-x^3+4x^2-x+3$

Now we find the x and y intercept of f(x)

For x-intercept: Put f(x)=0 and solve for x

So, x=3.92 (Just before 4 on x-axis)

For y-intercept: Put x=0 and solve for f(0)

So, y=3 (Passes through y-axis at 3)

End Behavior: Third degree function

$x\rightarrow -\infty , f(x)\rightarrow \infty$

$x\rightarrow \infty , f(x)\rightarrow -\infty$

Possible graph of the f(x). Please see the attachment.

Answer 2

Answer: Graph going through x axis just before 4  and passes through u axis at 3.

Step-by-step explanation:

Given : f(x)  = $-x^{3} +4x^{2} -x +3$.

To find : graph .

Solution : We have given that f(x)  = $-x^{3} +4x^{2} -x +3$.

We can see from the given polynomial leading coefficient is negative and degree is odd.

By the end behavior of polynomial function : left end of graph would be up and right would be down .

For y intercept ,  plug  x =0 in given function .

f(x)  = $-(0)^{3} +4(0)^{2} -(0) +3$.

f(x) = 3.

For x intercept , plug f(x) = 0.

0 =  $-x^{3} +4x^{2} -x +3$.

  x = 3.92

Therefore, Graph going through x axis just before 4  and passes through u axis at 3