Here the problem I cannot seem to solve: x varies inversely as x. Choose values for x and y. Use these values to write an equation. Then find y when x=5. Graph and state the domain and range.

Answer 1

A function where y varies inversely with x is the following: y=k/x where k is a constant.

The problem is asking to set up an equation like this where you create values of your own for y and x. Then you can solve the equation for k using algebra.

For example,

10=k/6

Using algebra to solve the equation, we can find that k=60. We can substitute that into our function to get

y=60/x

Now, we can plug in x=5 into our equation to find what y is when x=5:

y=60/5

y=12

Now, we can find the domain of our function. Since you can't divide by zero, our function is undefined at 0, so the domain is (-infinity, 0)U(0, infinity)

Now we can find the range of our function. Since the function is Bigger On Bottom (BOB), we know there is a horizontal asymptote at y=0, so we can see that our range is (-infinity, 0)U(0, infinity).