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

the graph of the function f(x)=(x - 4)(x + 1) is shown below. 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.

the graph of the function f(x)=(x - 4)(x + 1) is shown below. 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

Explanation:

Step1: Expand the function

$f(x)=(x - 4)(x + 1)=x^{2}-3x - 4$.

Step2: Find the vertex of the parabola

For a quadratic function $y = ax^{2}+bx + c$ ($a\neq0$), the x - coordinate of the vertex is $x=-\frac{b}{2a}$. Here $a = 1$, $b=-3$, so $x=-\frac{-3}{2\times1}=1.5$. Since $a = 1>0$, the parabola opens upward.

Step3: Analyze increasing and decreasing intervals

The function is decreasing on the interval $x<1.5$ and increasing on the interval $x > 1.5$.

Answer:

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