Question

The graph of the function f(x) = (x – 4)(x + 1) is shown below. On a coordinate plane, a parabola opens up. It goes through (negative 1, 0), has a vertex at (1.75, negative 6.2), and goes through (4, 0). Which statement about the function is true? The function is increasing for all real values of x where x < 0. The function is increasing for all real values of x where x < –1 and where x > 4. 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.

Answer 1

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

Explanation:

This is a vertical parabola open upward

The vertex is a minimum

The vertex is the point (1.5,-6.25)

we know that

The function is decreasing in the interval ----> (-∞,1.5) x < 1.5

That means----> the function is decreasing for all real values of x less than 1.5

The function is increasing in the interval ----> (1.5,∞) x> 1.5

That means----> the function is increasing for all real values of x greater than 1.5

see the attached figure to better understand the problem

therefore

The statement that is true is

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

Answer 2

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

Explanation:

we have

`f(x)=(x-4)(x+1)`

`f(x)=x^2+x-4x-4`

`f(x)=x^2-3x-4`

This is a vertical parabola open upward

The vertex is a minimum

The vertex is the point (1.5,-6.25)

we know that

The function is decreasing in the interval ----> (-∞,1.5) x < 1.5

That means----> the function is decreasing for all real values of x less than 1.5

The function is increasing in the interval ----> (1.5,∞) x> 1.5

That means----> the function is increasing for all real values of x greater than 1.5

see the attached figure to better understand the problem

therefore

The statement that is true is

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