The graph of the function
f(x)= (x-4)(x + 1) is shown below. which statement about the function is true?
a. the function is increasing for all real values of x wherex < 0
b. the function is increasing for all real values of x where
x < -1 and where x > 4
c. the function is decreasing for all real values of x where -1 < x < 4
d. the function is decreasing for all real values of x where
x < 1.5

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

Step-by-step explanation:

The vertex is at x=1.5, so the function is decreasing on one side of that and increasing on the other. Any answer choice with some number other than 1.5 as the boundary of increasing/decreasing can be ignored.

Of course one descriptor (increasing or decreasing) is not applicable for any interval that includes the point where the slope changes sign.

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

Step-by-step explanation:

The graph show a parabola, which is characterized for having decreasing and increasing interval, due to its behaviour.

In addition, decreasing means that while x-values increase, y-values decreases. On the other hand, increasing means that while x-values increase, y-values decrease.

You can observe in the graph that the function decreases, from negative infinite to x=1.5, and increases from x=1.5 to positive infinite. Based, on this deduction, we can say that the right answer is D, because it describes this decreasing behaviour for all x < 1.5, which is complete true.

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example 2 – simplify: step 1: completely factor both the numerators and denominators of all fractions. step 2: change the division sign to a multiplication sign and flip (or reciprocate) the fraction after the division sign; essential you need to multiply by the reciprocal. step 3 : cancel or reduce the fractions.