BOOK: The Official SAT Study Guide: For the New SAT
Three of these were careless mistakes. They were really easy and we don't need to go over them. I need to get rid of them!
1. The graph of y=f(x) is shown above. Which of the following could be the graph of y= f(x+2)?
I thought that the "dip" had to be on 2. But i guess that the inclined line has to be on 2.
2. If a,b,c and f are four nonzero numbers, then all of the following proportions are equivalent EXCEPT:
*a/f=b/c
*f/c=b/a
*c/a=f/b
*a/c=b/f
*af/bc=1/1
I tried the numbers 2,3,-2,-1 respectively, and none of the five answer choices worked! When they said a,b,c and f, did they mean 3 consecutive numbers?
3. For all numbers x and y, let the operation "circle" be defined by x "circle" y=xy-y. If a and b are positive integers, which of the following can be equal to zero?
I. a "circle" b
II. (a+b) "circle" b
III. a "circle"(a+b)
*I only
*II only
*III only
*I and II
*I and III
I tried two sets of numbers
7&1
3*4
none of them worked !!
What was i doing wrong?
3 comments:
I'm really proud of you for keeping up the work. You're really learning about the types of problems you're having difficulty with-- don't worry, you'll learn a lot of these in Alg 2 and stuff. Its just important to keep doing these problems over and over again for now.
1) Functions can be shifted over to the right, left, up, and down. Lets say there's a function f(x).
f(x)+1 moves the function down 1 unit
f(x)-1 moves the function up 1 unit
f(x+1) moves the function to the left
f(x-1) moves the function to the right 1 unit
This is testing your knowledge of that.
http://www.purplemath.com/modules/fcntrans.htm
This site is actually really good:
http://www.purplemath.com/modules/index.htm
You'll learn this all in Alg 2. No worries
2. No, they don't have to be consecutive. This is an odd-one-out situtaion where you have to figure out which answer choice doesn't fit in with the others
ok options C and D are the same-- they just flipped the fractions over. So those are definitely equivalent. A and B are not equivalent though, so one of them is definitely wrong. B and E match up and equal the same thing, so A is odd one out.
3. Opal, you can't just try numbers like that yet. Its more important to understand the relationships than blindly plug in. This is a MAJOR sticking point for you, and something you will have to work through.
First thing you want to do is rewrite the answer choices in terms of real variables using that function
I. A*B-B
II. (A+B)*B-B
III. A*(A+B)-(A+B)
Simplifying those, we get
I. A*B-B
II. AB+BB-B
III. AA + AB - A - B
Then, they're asking which of these can be equal to 0, assuming that they are positive integers. You can't plug in numbers here because they're not asking whether the numbers MUST be =0, but if there is some combination of positive integers out there that can make it 0
I. factors to B*(A+1)-- it can't ever be equal to 0
II. factors to B*(A+B-1) -- this can't ever be equal to 0 either.
III. Factor it to A*(A-1) + B*(A-1), or (A+B)*(A-1). If a=1, then the whole thing is equal to 0. III is the only possibility.
Kapil
i just came accross this in my own sat book. choice E is the right answer for 3. if a is 1 and b is 1, they will equal zero. Therefore, the correct answer is E
Kapil is wrong
f(x)+1 moves graph of function f(x) upwards.(i repeatv--upwards--).
f(x)-1 moves the graph of f(x) downwards.
check link for function graph changes study (especially for SAT)
http://cims.nyu.edu/~kiryl/Precalculus/Section_2.5-Transformations%20of%20Functions/Transformations%20of%20Functions.pdf
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