Question

I didn’t understand when my teacher taught this. Could you help show me how to solve this

Answer 1

The function given is,

$f\left(x\right)=\frac{x+6}{\left(x+12\right)^2}$

The graph of the function will be shown below

a) The zeros of a function, also referred to as roots or x-intercepts, occur at x-values where the value of the function is 0 (f(x) = 0).

Hence, from the graph above the zeros of the function is at

$x=-6$

b) The function's domain is

$\:\left(-\infty \:,\:-12\right)\cup \left(-12,\:\infty \:\right)$

c) The function's long-run behaviour is that:

$\mathrm{as}\:x\to \:+\infty \:,\:f\left(x\right)\to \:0$

Hence, the answer is

$0$