Does it matter which equation you use to plug the value of y into? Yes or No
2 answers:
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Firstly, we'll fix the postions where the women will be. We have
forms to do that. So, we'll obtain a row like:
The n+1 spaces represented by the underline positions will receive the men of the row. Then,
Since there is no women sitting together, we must write that . It guarantees that there is at least one man between two consecutive women. We'll do some substitutions:
The equation (i) can be rewritten as:
We obtained a linear problem of non-negative integer solutions in (ii). The number of solutions to this type of problem are known:
[I can write the proof if you want]
Now, we just have to calculate the number of forms to permute the men that are dispposed in the row:
Multiplying all results:
i. Domain and Range
The given function is
The domain of this function is,
The range refers to the y-values for which x is defined. x is defined for all values of y.
The range is all real numbers. See graph
ii. x-and-y-intercept
For x- intercept intercept we put
This implies that;
This will give us
The x-intercepts are
For y-intercept, we put
to obtain;
The y-intercept is
iii. Horizontal asyptote
Since degree of the numerator and the denominator are the same, there is a horizontal asymptote
To find the horizontal asymptote.
We divide the leading coefficient of the numerator by the leading coefficient of the denominator.
The horizontal asymptote is
iv. Vertical asymptote
To find the vertical asymptote, we equate the denominator to zero to get;
This implies that;
Split the middle term
Factor
Factor further
The vertical asymptotes are
