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?

A.all real values of x where x < −1
B.all real values of x where x < 1
C.all real values of x where 1 < x < 3
D.all real values of x where x > 3

Answer 1

There's an error in the graph, but the answer is A.

Answer 2

The correct option is A.

Explanation:

The given function is

`f(x)=(x-3)(x+1)`

Equate f(x)=0 to find the x-intercepts of the function.

`0=(x-3)(x+1)`

`x=3,-1`

The x-intercepts of the function are -1 and 3. From the below graph it is clear that,

In x<-1, the function is positive and decreasing.

In -1<x<1, the function is negative and decreasing.

In 1<x<3, the function is negative and increasing.

In x>3, the function is positive and increasing.

Therefore the correct option is A.