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

1 Answer
Dec 11, 2017

Answer:

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.