Explanation for Question 27 From the Math (Calc) Section on the 2020 March Sat
Now we're looking at question number 27, 2 which says that the function F is defined for all real numbers and the 3 graph Y equals F of X and the X, Y plane has a negative 4 slope. So which of the following must be true? 5 Okay. So if the Y or if the function F of X has 6 a negative slope, it'll look something like this, 7 right. It'll have a downwards pointing slope. 8 And then what else does it say? So it's defined for all real numbers. 9 That means that at every point on the graph, I do have a point 10 of the line. And so this is all we know, 11 all that we know really is that it has a negative slope, 12 and now we just need to go through each answer choice and see if 13 it's correct, or if it's incorrect. Now, 14 if we look at one, it says that a is less than B. 15 So I could think about putting a, somewhere in the negatives and be somewhere 16 in the positives, right? So here would be my point F of a, 17 and here would be my point FFP. And now it tells us the F 18 of a must be greater than F of B. 19 Right? I sure enough, in the graph it looks like F of a is 20 higher up than F of B. And so a are not necessarily 21 a, but one is going to be correct. 22 And so, even though we don't have the exact points for a and B, 23 we can kind of generalize them by simply picking a spot on the graph 24 where a is less than B to C. That one has to be a 25 correct answer. Right? So now we're looking at either a or C. 26 And if we look at C, it says that if a is greater than 27 zero, the...