Question

Given the graph of the function f(x) below what happens to f x when x is a very small negative number?

Answer 1

The correct option is b.

Explanation:

From the given graph it is noticed that the graph represents a parent rational function.

`F(x)=(1)/(x)`

As the value of x approaches towards a small negative number.

`lim_(x\rightarrow 0^-)F(x)=lim_(x\rightarrow 0^-)((1)/(x))`

`lim_(x\rightarrow 0^-)F(x)=(1)/(-0)`

`lim_(x\rightarrow 0^-)F(x)=-(1)/(0)`

`lim_(x\rightarrow 0^-)F(x)=-\infty`

It means the value of F(x) is very large number when x is a very small negative number.

From the given graph it is clearly seen that the F(x) is very large number when x is a very small negative number.

Therefore option b is correct.

Answer 2

We can see that function f(x) is heading to negative infinity. From graph we can see that it is heading to negative infinity faster and faster for small changes of x. Same goes for positive side of x axis only diference is of course is that f(x) is now going to positive infinity