kitchen table math, the sequel: progress report, part 2 & help desk

## Sunday, July 18, 2010

### progress report, part 2 & help desk

I started working on "SAT math" in earnest on 6-21-2010. At that point I was barely breaking 600 on practice tests.

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. Anonymous said...

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

David said...

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.

David said...

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. ChemProf said...

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). ChemProf said...

Sorry David, I posted before I fully read your second comment!

Catherine Johnson said...

thanks!