Question

the graph of ( f ) is shown below.
write an equation of the rational function that represents the graph.
( r(x) = )

Explanation:

Step1: Identify asymptotes

Vertical asymptote: $x=0$; Horizontal asymptote: $y=3$

Step2: Form basic rational function

General form: $R(x)=\frac{a}{x}+3$. Use intercept $(1,1)$:
$1=\frac{a}{1}+3$

Step3: Solve for $a$

$a=1-3=-2$

Step4: Finalize the function

Substitute $a=-2$ into the form.

Answer:

$R(x)=\frac{-2}{x}+3$ or $R(x)=3-\frac{2}{x}$