MATH SOLVE

5 months ago

Q:
# 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.

Accepted Solution

A:

Answer:The function is decreasing for all real values of x where x < 1.5.Step-by-step explanation:we have[tex]f(x)=(x-4)(x+1)[/tex][tex]f(x)=x^2+x-4x-4[/tex][tex]f(x)=x^2-3x-4[/tex]This is a vertical parabola open upwardThe vertex is a minimumThe vertex is the point (1.5,-6.25)we know thatThe function is decreasing in the interval ----> (-∞,1.5) x < 1.5That means----> the function is decreasing for all real values of x less than 1.5The function is increasing in the interval ----> (1.5,∞) x> 1.5That means----> the function is increasing for all real values of x greater than 1.5see the attached figure to better understand the problemthereforeThe statement that is true is The function is decreasing for all real values of x where x < 1.5.