Question

What are the excluded values for `y=7/(5x-10)`?

Answer 1

`x=2`

Explanation:

The only excluded values in this problem would be asymptotes, which are values of `x` that make the denominator equal to `0`. Since we cannot divide by `0`, this creates a point that is "undefined" or excluded.

In the case of this problem, we are looking for a value of `x` that makes `5*x-10` equal to zero. So let's set that up:
`5x-10=0`
`color(white)(5x)+10color(white)(0)+10`
`5x=10`
`/5color(white)(x)` `/5`
`x=10/5` or `2`

So, when `x=2`, the the denominator becomes equal to zero. So that's the value we must exclude to avoid an asymptote. We can confirm this using a graph
graph{y=7/(5x-10)}

See, the graph is getting closer and closer to `x=2`, but it can never reach that point.