Question

Graph the function. State the domain and range. Y=10/x-7 - 5

Answer 1

Consider the given function,

`y=(10)/(x+7)-5`

Note that there is a rational part of the function.

And for any rational expression, the denominator can never be zero. So we have to exclude the values for which the denominator becomes zero,

`\begin{gathered} x+7\\e0 \\ x\\e-7 \end{gathered}`

So the domain of the function will be the set of real numbers excluding the number -7 .

Since 'x' can never reach infinity, it follows that,

`\begin{gathered} (10)/(x+7)\\e0 \\ (10)/(x+7)-5\\e0-5 \\ y\\e-5 \end{gathered}`

So the range of the function will be the set of all real numbers excluding -5.