SOLUTION: \[f(x) = \frac{3x - 7}{x + 1} Find the domain and range of $f$, give answer interval form. Thank You!

Algebra ->  Functions -> SOLUTION: \[f(x) = \frac{3x - 7}{x + 1} Find the domain and range of $f$, give answer interval form. Thank You!      Log On


   

Question 1059941: \[f(x) = \frac{3x - 7}{x + 1}
Find the domain and range of $f$, give answer interval form.
Thank You!
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
f(x)=(3x-7)/(x+1)

f%28x%29=%283x-7%29%2F%28x%2B1%29

Zero at 7%2F3 and undefined at x=-1. 
INTERVAL                 EXAMPLE x      SIGN OF f(x)
-infinity%3Cx%3C-1                -3            (-)/(-)=(+), positive
-1%3Cx%3C=7%2F3                   0            (-)/(+)=(-), negative
7%2F3%3C=x%3Cinfinity                   4            (+)/(+)=(+), positive

The function has a horizontal asymptote of y=3.
Will f(x) ever be 3 ?
3x-7=3%28x%2B1%29
3x-7=3x%2B3----impossible to solve this. No solution.

RANGE: The real numbers such that system%28-infinity%3Cy%3C3%2CAND%2C3%3Cy%3Cinfinity%29
DOMAIN: Set of real numbers such that system%28-infinity%3Cx%3C-1%2CAND%2C-1%3Cx%3C=7%2F3%2CAND%2C7%2F3%3C=x%3Cinfinity%29


graph%28350%2C350%2C-12%2C6%2C-6%2C12%2C%283x-7%29%2F%28x%2B1%29%29