Mathematics
stboan13
17

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.

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(1) Answers
DanaeHowdyshell

Given the graph of the function f(x) = (x - 4)(x + 1). From the graph, it can be seen that the graph of the function describe a parabola facing up with the vertex at point (1.5, -6.25). The x-intercepts of the graph are at points (-1, 0) and (4, 0) while the y-intercept is at point (0, -4) The vertex of a parabola is the point in the parabola where the graph of the function stops decreasing and starts increasing, or vice-versa. Thus, the function stops decreasing at point (1.5, -6.25) and then starts increasing, this means that for values of x < 1.5 the function is decreasing and since 0 < 1.5, hence, the function is decreasing for the values of x < 0. Hence, the statement that "the function is increasing for all real values of x where x < 0" is not true. Similally, Given that the function stops decreasing at point (1.5, -6.5), this means that for values of x < 1.5 the function is decreasing and since -1 < 1.5, hence, the function is decreasing for the values of x < -1. Thus, the statement that the function is increasing for all real values of x where x < –1 and where x > 4  is not true. With the explanations given above, it can also be seen that the statement that "the function is decreasing for all real values of x where –1 < x < 4" is also not true.

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