Question

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

Answer 1

Consider the given function,

$y=\frac{10}{x+7}-5$

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,

$\begin{gathered} x+7\ne0 \\ x\ne-7 \end{gathered}$

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,

$\begin{gathered} \frac{10}{x+7}\ne0 \\ \frac{10}{x+7}-5\ne0-5 \\ y\ne-5 \end{gathered}$

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