Question

state the domain and range of the following: y = 3x/(2x-5)

Answer 1

Domain: (-infinity, 5/2)U(5/2, infinity)
Range: (-infinity,infinity)

Answer 2

range all real numbers except
\[\frac{3}{2}\]

Answer 3

no the range is all real numbers

Answer 4

Why is it all real numbers?

Answer 5

actually it is all real numbers except
\[\frac{3}{2}\] you can see it because there is no way for that ratio to be equal to 3/2. you are off by the -5 in the denominator

Answer 6

another way to say this is that the function has a horizontal asymptote at 3/2, and while it is possible for a function to cross its asymptote it does not in this case

Answer 7

o yea ur right

Answer 8

calculus will show that the function is strictly decreasing, but you do not need calculus to see that there is no way for this fraction to be equal to 3/2

Answer 9

how can you tell it will never equal 3/2?

Answer 10

its the coefficients of the "x"s

Answer 11

but only if the numerators and denominators exponents are equal

Answer 12

ok the numerator is 3x
the denominator is 2x-5
this ratio can never be equal exactly to 3/2 because whatever x is, it is the same on top and bottom. for the ratio to be exactly 3/2 that -5 would have to be gone

Answer 13

put say x = 100
you get 300/195 which is close to 3/2 but not exactly 3/2.

Answer 14

oh ok. Thank you very much