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The answer is the second option: Reciprocal; [tex]y=\frac{1}{x}[/tex].

The explanation for this exercise is shown below:

1. By definition, the a reciprocal function is represented by: [tex]y=\frac{1}{x}[/tex] and you can also write it in the following form: [tex]y=x^{-1}[/tex].

2. The graph of a reciprocal function has the form shown in the graph attached, which you can see it is a hyperbola and a odd function. Also, the function goes closer to the y-axis and x-axis but it does not touch them.  

Answer:

Reciprocal : [tex]y = \frac{1}{x}[/tex]                 Option B

Step-by-step explanation:

Given a graph and four options.

We check all the options one by one.

Option 1: Power y = xⁿ

Here n is any real number.

Graphs  of the form y = xⁿ all go through the point (1, 1)

The even powers, y = x⁰, x², x⁴ … also go through ( – 1 , 1)

and the odd powers, y = x¹, x³, x⁵… go through ( – 1 , – 1)

So I will use – 1 ≤ x ≤ 1 as the domain for each graph .

Option 2: Reciprocal  [tex]y = \frac{1}{x}[/tex]

Here y is inversely proportional to x.

its a rational function.

We see that for this function a small positive input value yields a large positive output value.

So this is correct.

Option B is correct.

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