Question

Write the formula of the function f(x) whose graph is shown.

Answer 1

`f(x)=(1)/(x+4)`

Explanation:

Asymptote: a line which the curve gets infinitely close to, but never touches.

From inspection of the graph, we can see that there is an asymptote at
`x=-4`, since the curve gets infinitely close to this line, but never touches it.

Therefore, the function is undefined at
`x=-4`

For a rational function to be undefined, the denominator must equal zero at that point. Therefore, we are looking for a rational function with a denominator that equals zero when
`x=-4`.

Therefore, option D is the correct solution, since:

`f(-4)=(1)/(-4+4)=(1)/(0) \implies \sf und efined`