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)=(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`