Tip #14 to Get a Top SAT Math Score (page 2)
Most students fear functions. "I suck at functions," I hear from almost every new student. I'm not sure where this attitude comes from, but here's the good news: functions on the SAT are easy. While functions could be the topic of a full-year university course, the SAT tests only two kinds of function questions. If you feared functions, the next two skills alone will earn you 3 more questions correct and raise your score 20 to 30 points!
Functions are just a type of equation, like y = mx + b. To show that an equation is a function, sometimes people replace the y with f(x>) or g(x) or h(x). That's it. Easy. To solve functions, remember that f(x) is just a fancy way of saying y. So f(x) = 2x –1 means the same as y = 2x –1.
Let's look at this question:
Solution: This is the first type of function question. This type simply asks you to plug the 3 in for x in the equation or graph. Cake! So f(3) = 2(3) + 1 = 7.
Correct answer: 7
Note: This type of function question might also ask you to use a graph instead of an equation to determine the answer. For example: If the line shown in the graph below is y = f(x), find f(3). Based on the graph, f(3) = 7, since when x = 3, y = 7.
- If f(x) = 2x3 – 2, what is the value of f(–2) ?
- For which of the following functions is f (5) < f (–5) ?
- f(x) = 2x2
- f(x) = 2
- f(x) = 2 – x3
- f(x) = x4 + 2
- The table above shows the values of the quadratic function f for selected values of x. Which of the following defines f ?
- f(x) = x2 + 1
- f(x) = x2 + 2
- f(x) = 3x2 – 2
- f(x) = 3x2 – 1
- f(x) = 3x2 + 1
- The total weekly soap use, in pints, from washing x cars is given by the function g(x) = 5x – (4x + k), where k is a constant. If last week 140 cars were washed, using 3 pints of soap, what is the value of k?
- If m(n) = n2 + 2n and h(n) = 2n2 – n, then m(6) – h(3) =
- The graph of y = f(x) is shown above. If f(3) = m, which of the following could be the value of f(m) ?
- A Simply plug – 2 in for x in the equation.
- D The long way to solve this question is to plug (5) and (–5) into each equation in the answer choices to see which one makes f(5) < f (–5). This absolutely works and is worth the time since it will earn you points. There is also a faster way. In every other answer choice, 5 plugged in for x will clearly give the same or higher value than when –5 is plugged in. However, choice D, f(x) = 2 – x3, is the only one where a positive number yields a lower result than a negative: 2 – 53 < 2 –(–5)3 –123 < 127.
- D This is a very common SAT question. Just choose an (x, y) point from the table and see which equation works. Choice D is correct since 11 = 3(2)2 – 1. Try all equations, in case several work. Then you would just choose a second point to find the one answer choice that works for both points.
- E This is a very typical SAT question, appearing on nearly every SAT. If you got this question wrong and you spend the time to master it, you will gain points! In this question, you are given values for the number of cars, which is x, and for pints of soap, which is g(x). g(x) = 140 and x = 3. Simply plug these values in for x and g(x), and use basic algebra to solve for k. If this is confusing, redo this question over and over until you can teach it to a friend. Then do that! This is a great party question. Next time you go to a party, bring this one, people love it. OK, I'm kidding.
- g(x) = 5x – (4x + k)
- 3 = 5(140) – (4(140) + k)
- 3 = 700 – 560 – k
- 3 = 140 – k
- –137 = –k
- 137 = k
- D Plug 6 into the m function, plug 3 into the h function, and subtract the results.
- E f(3) means "plug 3 in for x" and get y. Usually we use an equation to answer this, but in this question we use the graph shown. We simply locate x = 3 on the graph and see what the y value is at that point. y = –2. Then the question asks for f(–2), so we look on the graph once again, but this time we plug –2 in for x. The best answer is y = .
f(–2) = 2(–2)3 – 2 = –18.
Go to: Tip #15
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