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3 years ago

Which of the following rational functions is graphed below?

Mathematics

2 answers:

AlekseyPX3 years ago

6 0

Answer:

The rational function that is graphed is B

navik [9.2K]3 years ago

5 0

<h2>Answer:</h2>

The rational function which is graphed below is:

Option: B

B. $F(x)=\dfrac{x}{(x-1)(x+1)}$

<h2>Step-by-step explanation:</h2>

From the graph of the function we see that the graph has vertical asymptote at x=1 and x= -1

Also, we know that while finding the vertical asymptote of the rational function we substitute denominator equal to zero and the values of such x will be the vertical asymptote.

Also, if the line y=0 act as a horizontal asymptote if the degree of polynomial in numerator is smaller than in the denominator.

The function in which above two property hold true is:

B. $F(x)=\dfrac{x}{(x-1)(x+1)}$

( since in option: A

If denominator equal to 0 then x=0 and -1

This means that the vertical asymptotes are 0 and -1 .

In option: C

If denominator is equal to zero.

Then x=0 and 1

This means that the vertical asymptotes are 0 and 1

In option: D

When denominator=0

then x=0

This means that the vertical asymptote is at x=0

which is false )

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Answer:

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Step one:

given data

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Step two:

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3 years ago

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Factor the polynomial, x2 + 5x + 6

patriot [66]

Answer:

Choice b.

$x^{2} + 5\, x + 6 = (x + 3)\, (x + 2)$ .

Step-by-step explanation:

The highest power of the variable $x$ in this polynomial is $2$ . In other words, this polynomial is quadratic.

It is thus possible to apply the quadratic formula to find the "roots" of this polynomial. (A root of a polynomial is a value of the variable that would set the polynomial to $0$ .)

After finding these roots, it would be possible to factorize this polynomial using the Factor Theorem.

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Similarly:

$\begin{aligned}x_{2} &= \frac{-5 - \sqrt{1}}{2\times 1} \\ &= \frac{-5 - 1}{2} \\ &= -3\end{aligned}$ .

By the Factor Theorem, if $x = x_{0}$ is a root of a polynomial, then $(x - x_0)$ would be a factor of that polynomial. Note the minus sign between $x$ and $x_{0}$ .

The root $x = -2$ corresponds to the factor $(x - (-2))$ , which simplifies to $(x + 2)$ .
The root $x = -3$ corresponds to the factor $(x - (-3))$ , which simplifies to $(x + 3)$ .