Tip #14 to Get a Top SAT Math Score

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.

Example Problems

Easy

1. If f(x) = 2x³ – 2, what is the value of f(–2) ?
   1. –18
   2. –16
   3. –10
   4. 8
   5. 24

Medium

2. For which of the following functions is f (5) < f (–5) ?
   1. f(x) = 2x²
   2. f(x) = 2
   3. 
   4. f(x) = 2 – x³
   5. f(x) = x⁴ + 2



3. The table above shows the values of the quadratic function f for selected values of x. Which of the following defines f ?
   1. f(x) = x² + 1
   2. f(x) = x² + 2
   3. f(x) = 3x² – 2
   4. f(x) = 3x² – 1
   5. f(x) = 3x² + 1
4. 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?
   1. –137
   2. –31
   3. 1
   4. 31
   5. 137
5. If m(n) = n² + 2n and h(n) = 2n² – n, then m(6) – h(3) =
   1. 0
   2. 15
   3. 25
   4. 33
   5. 52

Hard



6. The graph of y = f(x) is shown above. If f(3) = m, which of the following could be the value of f(m) ?
   1. 
   2. 3
   3. 0
   4. –3
   5.