Question

What is 2x^2+7x-4/x^3 -1

Answer 1

Domain is the numbers you can use
you can't use any numbers that make an impossibility like a negative square root or dividing by 0

set the denomenator equal to 0 to find what values of x make it 0
x^3-1=0
add 1 both sides
x^3=1
cube root both sides
x=1
domain is all real numbers except for 1
range is the numbers you get from inputing domaain
there is a vertical assemtote there so all bases are covered
range is how high and low y goes
domain is how far left and right x goes


domain is all real numbers except x=1
range is all real numbers

Answer 2

Find vertical and horizontal asymptotes
vertical: set denominator=0
x^3-1=0
x^3=1
VA=1

horizontal: highest degree of num. < highest degree of den.
HA=0

domain and range
d: (-infinity, 1)U(1, infinity)
r: (-infinity, 0)U(0, infinity)