# What is the domain and range of #y = (x+1)/(x^2-7x+10)#?

##### 1 Answer

See below

#### Explanation:

Firstly, the domain of a function is any value of

Therefore, in this case, the domain is where the denominator is equal to

This is

If we factorise this, we get

So therefore, the domain is all values of

To find the range of a rational function, you can look at its graph. To sketch a graph, you can look for its vertical/oblique/horizontal asymptotes and use a table of values.

This is the graph graph{(x+1)/(x^2-7x+10) [-2.735, 8.365, -2.862, 2.688]}

Can you see what the range is? Remember, the range of a function is how much you can get out of a function; The lowest possible