Question

Plot the graph of a function $f\left(x\right)=\frac{2x+1}{x-2}$ and find $x$ and $y$ intercept of $f\left(x\right)$.

• A. $(-\frac{1}{2},0)$ and $(0,-\frac{1}{2})$
• B. $(-1,0)$ and $(0,-\frac{1}{2})$
• C. $(-\frac{1}{2},0)$ and $(0,-1)$
• D. $(-1,0)$ and $(0,-1)$

Answer 1

The correct option is A $(-\frac{1}{2},0)$ and $(0,-\frac{1}{2})$

$f\left(x\right)=\frac{2x+1}{x-2}$

For $y$ intercept $x=0$

$\Rightarrow y=\frac{2\left(0\right)+1}{0-2}=-\frac{1}{2}$

So the point on the $y$ axis is $(0,-\frac{1}{2})$

For $x$ intercept $y=0$

$\Rightarrow \frac{2x+1}{x-2}=0\Rightarrow 2x+1=0\Rightarrow x=-\frac{1}{2}$

So point on $x$ axis is $(-\frac{1}{2},0)$

So option $A$ is correct.