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Today - 7-18-2010 - I answered all of the questions in "score bands" 600-690 and 700-800 posted on the SAT Skills Insight page.
results:
600-690 range:
40 questions
39 correct
(I missed a circle question because I have yet to review circles.)
700-800 range:
30 questions
20 correct
help desk
Question number 1 in Skill Group 6, Score Band 700 - 800
The graphs of the functions
and 
are lines, as shown in the figure above. If 
for some constants 
and 
, which of the following could define the function 
?I'm stumped.
5 comments:
This question is clearly intended as multiple choice. The two obvious observations are that g has a higher slope than f, and that g's y intercept is smaller. Also, g's y-intercept seems to be negative rather than positive, and both slopes are positive.
I'd look for something like g=2mx-b
f and g are inverse functions. Solving y = mx + b for x yields x = y/m - b/m, so g(x) = x/m - b/m.
Of course, we can't deduce from the picture that g is the inverse of f, although it appears to be. Answers A and B can be eliminated because they are parallel to y = f(x). C is wrong because it has a positive y-intercept, and E is wrong because it has a negative slope.
The possible answers are:
a. g(x) = mx -b
b. g(x) = mx + b/m
c. g(x) = 1/m x + b
d. g(x) = 1/m x -b/m
e. g(x) = -1/m x -b
You can't just solve it. You need to look at the possible answers.
a and b are out because the lines aren't parallel so don't have the same slope.
e is out because both slopes are positive. So it is either c or d.
c would have both lines crossing y = 0 at the same point, so the answer must be d (which fits, as the intercept of the g(x) line is negative).
Sorry David, I posted before I fully read your second comment!
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