SAT Question of the day – Nov 05

Here is the SAT question of the day for Nov 05 2012 and my suggested approach to solving it.

If the graph of the function function f in the x times y-plane contains the points (0 comma negative 9), (1 comma negative 4), and (3 comma 0), which of the following CANNOT be true?

A.     The graph of function f has a maximum value.

B.     y less than or equal to 0 for all points (x comma y) on the graph of function f.

C.     The graph of function f is symmetric with respect to a line.

D.     The graph of function f is a line.

E.     The graph of function f is a parabola.

 

Now – let see what this question is really about!

It is a “What can’t be” question because it asks

“What CANNOT be true?”

Which mean we need to know something about each option.

There are 3 points of a function that are given to us and from their coordinates we need to conclude something about the function.

What happens between the points given? who knows? depends on the function.

It is now wise to remember that in the SAT

the answers are part of the question ! 

we know (or I hope you know) that a line is defined by two points. This seems the most easy option to disprove. If the rise between X=0 to X=1 is 5 =[-4-(-9)] then if we move another two units to the right (to get to X=3 – our run) we should add another 10 units to the rise and get to [10+(-4)]=6 but when X=3 we have 0 – which means these three points are not on a line- QED

Now lets look on the other options – the idea is that a. we can learn something b. we are not always going to be smart and check the option that is the right answer first.

All we need to find or imagine is a case in which these points will fulfill the statement – remember the way this question is phrased means we are looking for an answer that is always NOT TRUE.

A.     The graph of function f has a maximum value.

Could be – if it starts at -9 goes up to -4 and continue to 0 – it makes sense it has a maximum somewhere. Those of you who have taken Calculus can relate to some of the fundamental theorems of Calculus !

So we agree this is not always wrong (in fact it is always true)

B.     y less than or equal to 0 for all points (x comma y) on the graph of function f.

Well lets see – we have three y values:  -9, -4, and 0 all are equal or smaller than zero. It is possible the graph never crosses the X axes – Does the graph have to cross the X axes and have values greater than zero? NO – so this statement is not always false and can be at some instances true and thus we can cross it out.

C.     The graph of function f is symmetric with respect to a line.

WHAT? well lets think what this statement  means. Draw a few points on the bottom half of a piece of paper and connect them. Now fold the paper in the middle and copy the points to the upper part of the paper. Connect the points on the top part. You just created a symmetric function with respect to the line created by you folding the paper.

Now can you imagine you can do the same with the 3 points given? probably yes – so this option goes away because it can be true and is not always false.

D.     The graph of function f is a line.

We discussed this is impossible. and this is the answer to choose.

E.     The graph of function f is a parabola.

Well, is the graph of a parabola (y=aX^2+bX+c) can be drawn to include these points? yes – we can imagine a part of a parabola passing through any three given points – just sketch them and see.

 

Notice we have all the types of answers here – the correct one – an answer that can never be

Answers that are always true and answers that can be true but are not necessarily so.

Be ready for this kind of a mix. Read the answers as part of your reading of the question and always start with the one that look the most easy to check.

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