Transformation of graph of $f(x)$ to $\frac{1}{f(x)}$

Question

With the help of the graph given below i.e. $y = f(x)$ plot the graph of :-

$1.$ $y=\frac{1}{f(x)}$

$2.$ $y=2f(x)$

$3.$ $y=f(2x)$

For $y=2f(x)$, I multiplied each coordinate of $y$-axis by 2 and for $y=f(2x)$ each coordinate of $x$-axis by $\frac{1}{2}$ which I think is correct. Could some help me with the transformation $f(x) \to \frac{1}{f(x)}$ ${}{}{}$

Answer 1

Hint: If y=$f(x_0)=0$ then $y=\frac1{f(x_0)}=\pm\infty$

Answer 2

Hint: Find the equation for each line, take its reciprocal and graph it. Make sure to find the domain restriction for each line and apply it to their reciprocal. Note that if $f(x_m)=0$ then $\lim_{x\to\pm{x_m}}\frac{1}{f(x)}=\pm\infty$