Answer Choices
2
0
−2
−3
Explanation for Question 30 From the Math (Calc) Section on the Official Sat Practice Test 4
So now we're looking at question number 30, which gives us a nice graph 2 right here. Right? So we're told that the function F of X is right 3 here, and this is what it's been graphed for us. And K is a 4 constant such that F of X equals K has three real solutions. 5 All right. So let's, let's talk about this first off, if F of X 6 equals K is a constant and we know F of X is kind of 7 like saying Y then we're saying that Y is a constant and 8 a normal number, just a normal number that never changes. 9 For example, we say Y is equal to two. And so what that means 10 is that we really have a horizontal line here at some point, 11 if it was, Y is equal to, we have a horizontal line going through 12 two, so that no matter what X you're at, 13 if you go up your Y value is always that number, 14 right? 15 Your Y value is always constant. And so we're told here that, 16 um, this equation has three real solutions, 17 and we can think about what solutions are, right. 18 If we think about systems of equations, 19 when we solve for solutions, for those, we're really looking for intersection points, 20 right? And so if I have three real solutions, 21 then that means that my F of X here and this F of X 22 intersect with each other three times. So what that means is that I need 23 to find a K or a value of Y where if I were to 24 draw a horizontal line, I would hit this graph three times. 25 And that happens somewhere around here, right in the bottom part where I have 26 1, 2, 3 intersections. 27 If I were to go at positive two, I'd only hit it once. 28 If I were to go zero again, I'd only hit at once. 29 If I were to go negative two, still a little too high, 30 I'd only hit it once, but it negative three, 31 where I go through right about here, 32 we hit it three times getting us those three solutions, 33 making our best answer D.