The graph of the function f(x)=(x-4)(x+1) is shown below. which statement about the function is true?

(1) the function is increasing for all real values of X where X < 0

(2) the function is increasing for all real numbers of x where X < -1 and x>4

(3) the function is decreasing for all real numbers of x where x< 1.5

(3) the function is decreasing for all real numbers of x where x< 1.5

Step-by-step explanation:

The function given in this problem is

which can be rewritten as:

A function is:

- Increasing over a certain interval if the first derivative is positive in that interval

- Decreasing over a certain interval is the first derivative is negative in that interval

So we start by calculating the first derivative of this function. We get:

This function is positive when:

Which means, when x > 1.5.

So the function is:

- Increasing for x > 1.5

- Decreasing for x < 1.5

So the correct option is

(3) the function is decreasing for all real numbers of x where x< 1.5

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