Question

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

Answer 1

See below

Explanation:

Firstly, the domain of a function is any value of `x` that can possibly go inside without causing any errors such as a division by zero, or a square root of a negative number.

Therefore, in this case, the domain is where the denominator is equal to `0`.
This is `x^2-7x+10=0`
If we factorise this, we get
`(x-2)(x-5)=0`
`x=2, or x=5`

So therefore, the domain is all values of `x` where `x!=2` and `x!=5`. This would be `{x inRR| x!=2, x!= 5}`

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 `y` value to the highest possible `y` value.