Answer to Question #266014 in Algebra for JOYCE ANTONETTE

Question

f(×)=3/×+4

Answer 1

Analyzing the given function

1) Domain

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

$x<0$ or $x>0$

2) Range

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

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

$xy=3+4x$

$x(y-4)=3$

$x=\frac{3}{y-4}$ $y$ cannot be $4$

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

3) Asymptotes

Vertical asymptote is $x=0$

Horizontal asymptote $y=4$

4) Zeros

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

$3+4x=0$

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

Graph of the function