Question #266014

f(×)=3/×+4


1
Expert's answer
2021-11-15T17:48:57-0500

Analyzing the given function

1) Domain


f(x)=3+4xxf(x)=\frac{3+4x}{x} xx cannot be zero


x<0x<0 or x>0x>0




2) Range


f(x)=3+4xxf(x)=\frac{3+4x}{x}


Let y=3+4xxy= \frac{3+4x}{x}


xy=3+4xxy=3+4x

x(y4)=3x(y-4)=3

x=3y4x=\frac{3}{y-4} yy cannot be 44


\therefore Range is f(x)<4f(x)<4 or f(x)>4f(x)>4


3) Asymptotes


Vertical asymptote is x=0x=0


Horizontal asymptote y=4y=4


4) Zeros


3+4xx=0\frac {3+4x}{x}=0


3+4x=03+4x=0

    4x=3x=0.75\implies \>4x=-3\\x=-0.75


Graph of the function









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