Question

What is the range of the function `f(x) = (3x-4)/(1+2x)`?

Answer 1

The range is `=RR-{3/2}`

Explanation:

As you cannot divide by `0`, `1+2x!=0`, `=>`, `x!=-1/2`

The domain of `f(x)` is `D_f(x)=RR-{-1/2}`

`lim_(x->+-oo)f(x)=lim_(x->+-oo)(3x)/(2x)=lim_(x->+-oo)3/2=3/2`

There is a horizontal asymptote `y=3/2`

Therefore the range is `R_f(x)=RR-{3/2}`

graph{(y-(3x-4)/(1+2x))(y-3/2)=0 [-18.02, 18.01, -9.01, 9.01]}