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 (neg
ative 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.
2 answers:
Answer:
The function decreases across all real numbers x where x < 1.5.
Step-by-step explanation:
We have
This represents an upward-opening vertical parabola
The vertex denotes a minimum point
The vertex is located at (1.5,-6.25)
We know that
The function is decreasing within the interval ----> (-∞, 1.5) x < 1.5
This means----> the function is continuously decreasing for all real x values under 1.5
Conversely, the function is increasing within the interval ----> (1.5, ∞) x> 1.5
Thus, for all real x values greater than 1.5, the function is increasing
Check the attached figure for further clarification
Therefore
The true statement is
The function decreases across all real numbers x where x < 1.5.
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Answer:
(B) There is a single solution: x = 0.
Step-by-step explanation:
The equation that Kate is attempting to solve is:
Consequently, this equation results in one solution: x = 0.