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According to the graph of the rational function y-
2
x2 = 1
which of the following statements is/are true?
1. The function is odd.
II. The function is decreasing for all values in the domain
III. There is a horizontal asymptote along the x-axis.

UMMMM… HELP !

According to the graph of the rational function y 2 x2 1 which of the following statements isare true 1 The function is odd II The function is decreasing for al class=

Respuesta :

Answer:

I think the answer would be I and II.

Step-by-step explanation:

I can't remember what makes an even or odd function. But we know 2 is true because there's no negative, so it can't be decreasing. And I think 3 is false because the bottom becomes (x+1)(x-1), but nothing cancels, so those have to be horizontal asymptotes. So, I think it's I and II.

There is a horizontal asymptote along the x-axis at x = -1 and x = 1

What is the period of a function?

The distance between the repetition of any function is called the period of the function.

What is a odd function?

The odd functions are functions that return their negative inverse when x is replaced with –x. This means that f(x) is an odd function when f(-x) = -f(x).

What is asymptote?

An asymptote is a line that the graph of a function approaches as either x or y go to positive or negative infinity.

According to the given question.

We have a function

[tex]y = \frac{2}{x^{2} -1}[/tex]

If we draw the graph of the given function.

The graph is symmetric on y axis. So, the function is even.

Or we can also check by replacing x by -x.

[tex]f(-x) = \frac{y}{(-x)^{2}-1 }=f(x)[/tex]

Therefore, the given function is even.

In the interval (-∞, -1) and (-1, 0) the function is increasing. And in the interval {0, 1) and (1, +∞) the function is subtracting. Hence, the function is not decreasing for all the values in the domain.

There is a horizontal asymptote along the x-axis at x = -1 and x = 1.

Hence, only option III is correct.

Find out more information about increasing, decreasing, even, odd and asymptote of the function here:

https://brainly.com/question/12191454

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