Functions

Remember that your goal is to get as many questions right as possible, not to answer as many as you can. In some cases, leaving a question blank can be better for your score than guessing, but best of all is to solve the problems efficiently and confidently enough that you can answer every question right. Solve each problem as if it did not have answer choices by reading carefully, noting the bottom line, assessing your options, attacking the problem, and looping back to double-check your answer.

In the xy - plane, line l is perpendicular to the graph of the function f(x) = 5x - 2. Line l could be the graph of which of the following functions?

Your bottom line in this case is "Which of the following?" In WOTF questions, always check E first and work your way back up to A. WOTF questions are much more likely than normal questions to have D or E coded as the correct answer. (The exception to this is Roman Numeral questions, in which the actual answer choices will say things like A) I and II, B) II only, etc. These are random.)

Next, assess your options. You could guess, and since this is a "which of the following" question, you would be relatively safe in guessing D or E. Or you could work from what you know to make a prediction about the correct answer.

You should know that the slope of any line is the negative reciprocal of the line perpendicular to it. That is, if the first line has a slope of m, the second line has a slope of $-\frac{1}{m}$. You should also know that slop-intercept the formula for a line is y = mx + b. Since the equation in the problem is f(x) = 5x - 2, the slope of the given line is 5. Therefore, the slope of the perpendicular line is $-\frac{1}{5}$.

Now look at the answer choices:

A) g(x) = -5x

B) $g(x)=-\frac{1}{5}x$

C) g(x) = x - 2

D) $g(x)=\frac{1}{5}x$

E) g(x) = 5x

The only option that has the correct slope is B. That is the correct answer. Remember that rules of thumb, like starting with E on WOTF questions, are not always reliable.

On sat.collegeboard.org, 62% of responses were correct.

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