Instead of reaching instinctively for your calculator, first take a brief look at each question and understand exactly what it's asking you to do. That short pause will save you a great deal of time later on. For example, what if you came upon the question:
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If (3, y) is a point on the graph of f(x) = , then what is y? |
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(A) |
–3 |
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(B) |
–1.45 |
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(C) |
0 |
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(D) |
.182 |
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(E) |
4.87 | |
A trigger-happy calculator user might immediately plug in 3 for x. But the student who takes a moment to think about the problem will probably see that the calculation would be much simpler if the function was simplified first. To start, factor 11 out of the denominator:
Then, factor the numerator to its simplest form:
The (x – 4) cancels out, and the function becomes f(x) = (x – 1) ⁄ 11. At this point you could shift to the calculator and calculate f(x) = (3 – 1) ⁄ 11 = 2/ 11 = .182, which is answer D. If you were very comfortable with math, however, you would see that you don't even have to work out this final calculation. 2⁄11 can't work out to any answer other than D, since you know that 2⁄11 isn't a negative number (like answers A and B), won’t be equal to zero (answer C), and also won't be greater than 1 (answer E).
