Question

on the graph below draw the horizontal asymptote and write the equation for the horizontal asymptote underneath. $f(x)=\frac{3}{x - 1}$ on graph below, draw the the vertical asymptote and write the equation for the vertical asymptote underneath. $f(x)=\frac{3}{x - 1}$

Explanation:

Step1: Find horizontal asymptote

For a rational function $f(x)=\frac{a}{x - b}$ (where $a$ and $b$ are constants), as $x\to\pm\infty$, the value of $y$ approaches $0$. So for $f(x)=\frac{3}{x - 1}$, the horizontal - asymptote is $y = 0$.

Step2: Find vertical asymptote

Set the denominator equal to zero. For $f(x)=\frac{3}{x - 1}$, when $x-1=0$, we have $x = 1$. So the vertical asymptote is $x = 1$.

Answer:

Horizontal Asymptote (Equation): $y = 0$
Vertical Asymptote (Equation): $x = 1$