Question

For each of the functions below, describe the domain of definition that is understood: f(z) = (1/x²)+1

Answer 1

Answer: x
`\\eq` 0

Explanation:

The domain of a function consists of the x-values that have a y-value in a function. The +1 shifts the graph upwards 1 unit. This only affects the range, the y-values. The x is in the denominator of a function, and the denominator of a function can never be 0, so we can say x
`\\eq` 0. There are no other restrictions on the domain; x can be negative, x can be positive, but x cannot be 0.

If we graph this function, we'll see that there are no y-values when x = 0. We say that there is a vertical asymptote at x = 0, an imaginary line at an x-value that does not have any y-values.

I hope this helps! :)