Question

The graph of the function f(x) = (x − 3)(x + 1) is shown. Which describes all of the values for which the graph is positive and decreasing?

Answer 1

All real values of x where x < −1

Explanation:

Answer 2

All real values of x where x < −1

Explanation:

Solve the function as an inequality:

(x-3)(x+1)>0

There are two cases in this:

Both factors are greater than 0.

x-3>0 and x+1>0

x>3 and x>-1

The intersection is x >3

OR

Both factors less than 0.

x-3<0 and x+1<0

x< 3 and x<-1

The intersection is x< -1

We have obtained that the function is positive for the intervals x < -1 and x > 3. But in one of those intervals the function is decreasing and in the other is increasing.

The answer is: all real values of x where x < −1 ....