Question

Which statement about the function is true?

The graph of the function f(x) = (x - 4)(x + 1) is shown
below.
The function is increasing for all real values of x
where
x<0.
O The function is increasing for all real values of x
where
x < -1 and where x>4
6
4-
2
O The function is decreasing for all real values of x
where
-1<x<4.
The function is decreasing for all real values of x
where
x < 1.5.
2
4
6
-6-4-2
-2
X
27
4
6​

Answer 1

The correct option is:

The function is decreasing for all real values of x where x < 1.5.

Explanation:

We are given a function f(x) which is a product of two linear polynomial as:

Now, we know that on multiplying the two linear polynomial we will obtain a quadratic polynomial.

So, the function f(x) will be represented as:

So, we will plot the graph of the function and check which statements about the function hold true.

1)

The function is increasing for all real values of x where x < 0.

This statement is false.

Since we get from the graph that function f(x) is decreasing for x<0.

2)

The function is increasing for all real values of x where x < –1 and where x > 4.

This option is incorrect as the function is decreasing for x<-1

whereas it is increasing for x>4.

3)

The function is decreasing for all real values of x where –1 < x < 4.

This option is incorrect.

Since, the function is both decreasing as well as increasing in the interval (-1,4).

4)

The function is decreasing for all real values of x where x < 1.5.

This option is correct.

Since it could be observed from the graph that the function is decreasing for x<1.5.