Question

Suppose that x and y vary inversely, how do you write a function that models inverse variation given $x=1$ and $y=11$?

Answer 1

We start solving the problem by recalling the fact that if the variables x and y are varied inversely, then they satisfy the condition $xy=c$. We then substitute the given values of x and y in this condition to proceed through the problem. We then make the necessary calculations to get the value of c which gives the required function for the given problem.

Complete step-by-step answer:
According to the problem, we are asked to write the function that models inverse variation given $x=1$ and $y=11$ if the variables x and y are inversely varied.
We know that if the variables x and y are varied inversely, then they satisfy the condition $xy=c$ ---(1). Let us substitute the given values of x and y in this relation to proceed through the problem.
So, we have $1\times 11=c$.
$\Rightarrow c=11$ ---(2).
Let us substitute equation (2) in equation (1).
So, we get $xy=11\Leftrightarrow y=\dfrac{11}{x}$.
So, we have found the function representing the relation between the given variables x and y as $xy=11$ or $y=\dfrac{11}{x}$.
$\therefore$ The function representing the relation between the given variables x and y is $xy=11$ or $y=\dfrac{11}{x}$.

Note: Whenever we get this type of problems, we first recall the relations that were satisfied by the given condition. We should not make calculation mistakes while solving this type of problem. We can also plot the obtained function by finding the points on the given curve. Similarly, we can expect problems to find the asymptote of the given function.