What is the domain and range of f(x)=(x^2-9)/(x^2-25)?
1 Answer
Jun 28, 2017
Explanation:
The denominator of f(x) cannot be zero as this would make f(x) undefined. Equating the denominator to zero and solving gives the values that x cannot be.
"solve " x^2-25=0rArr(x-5)(x+5)=0
rArrx=+-5larrcolor(red)" are excluded values"
rArr"domain is " x inRR,x!=+-5
"to find any excluded value in the range we can use the"
"horizontal asymptote"
"horizontal asymptotes occur as"
lim_(xto+-oo),f(x)toc" ( a constant)" divide terms on numerator/denominator by the highest power of x, that is
x^2
f(x)=(x^2/x^2-9/x^2)/(x^2/x^2-25/x^2)=(1-9/x^2)/(1-25/x^2) as
xto+-oo,f(x)to(1-0)/(1-0)
rArry=1" is the asymptote and thus excluded value"
rArr"range is " y inRR,y!=1
