given the rational function 1 x <mrow class="MJX-TeXAtom-ORD">

enrotlavaec

enrotlavaec

Answered question

2022-06-21

given the rational function 1 x 2 x 2 3 and asked for the domain and range, I multiplied thru by 2 and got 2 2 x 2 x 6 I understand the domain includes all real numbers except for (vertical asymptotes) 3 2 and 2. i thought there were no horizontal asymptotes until I graphed it on a calculator. according to the calculator the range is ( , 16 49 ] ( 0 , ). this makes sense to me looking at the graph but how can I obtain these results for the range using algebra? thank you

Answer & Explanation

Haggar72

Haggar72

Beginner2022-06-22Added 25 answers

First, we need to find the roots of the denominator and the range of the denominator.
We denote the denominator as f.
f = x 2 1 2 x 3 = 0 has roots x 1 = 2 and x 2 = 3 2 . So the domain is the real line excluding the two roots.
Next we need to find the range.
49 16 < x 2 1 2 x 3
49 16 < f
To find the range of the rational function is to find the range of 1 f .
I'll leave it to you.

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