Cracking the SAT subject test in math 2, 2nd edition

Cracking the SAT Subject Test in Math 2, 2nd Edition (A) ¥7 (B) ¥8 (C) ¥9 (D) ¥10 (E) ¥11 21 §1 + §2 + §3 §100 + §101 = (A) −151 (B) −51 (C) 0 (D) 50 (E) 51 FUNCTIONS USING STANDARD NOTATION On many q[.]

(A) ¥7 (B) ¥8 (C) ¥9 (D) ¥10 (E) ¥11

21 §1 + §2 + §3…§100 + §101 =

(A) −151 (B) −51 (C) 0 (D) 50 (E) 51

FUNCTIONS USING STANDARD NOTATION

On many questions, ETS will also give you functions with letters, such as f and g, that look like the ones you’ve probably studied in school A

function is a type of relation between two sets of numbers called the domain and range of the function Specifically, a function is a relation in which every element in the domain corresponds to only one element in

the range; for every x in the function, there is only one possible f(x) (or y,

on a graph)

The most basic function questions test only your understanding of functions and the algebra required to work with them Here are some examples of basic functions

The best way to think of function is that it’s like a machine It spits out a different result depending on what you put into it As long as you follow the directions of the machine, it will spit out the right response for you The test may bring up a couple of phrases: independent variable and

dependent variable The independent variable is what you put into the

machine You could put anything in; it doesn’t rely on anything, so it’s

independent The dependent variable is what your machine spits out.

What it is depends on what’s put into the machine That’s why it’s the

dependent variable On a graph, the independent variable is on the x-axis

and the dependent variable is on the y-axis.

f(x) = y

Sometimes it helps to think of f(x) as being equal to y Both are the result you get when

you put a number into the equation.

When questions ask you to work with algebraic functions, you’ll be required to do one of two things: plug numbers into a function and get a numerical answer, or plug variables into a function and get an algebraic

answer For example, given the function g(x) = (x + 2)2, you could run into two types of questions:

1 If g(x) = (x + 2)2, what is the value of g(4) ?

(A) 8 (B) 12 (C) 16 (D) 36 (E) 64

Here’s How to Crack It

Answering this question is a simple matter of plugging 4 into the

The Rare Occasion

There are a few unusual function types that you should be prepared for It is possible, for example, for elements in the domain to consist

of more than one value, like this:

In each of these functions, an element in the domain is a pair of values Functions of this kind are fairly rare on the SAT Subject Test

in Math 2, but you may run into one Although they’re unusual, they’re not difficult Simply treat them like ordinary functions—to

calculate the value of f(3, 4), for example, simply take the values 3

and 4 and plug them into the definition of the function in the

positions of a and b, respectively (you get )

Here, on the other hand, is an algebraic version of the same question:

3 If g(x) = (x + 2)2, what is the value of g(x + 2) ?

(A) x2 + 4

(B) x2 + 6

(C) x2 + 4x + 4 (D) x2 + 4x + 6 (E) x2 + 8x + 16

To solve this question, just Plug In a number for x Let’s pick x = 3, and plug that into g(x + 2) You need to find g(3 + 2) = g(5), which is (5 + 2)2

= 49, our target number Now, plug x = 3 into the answer choices, to see

which one turns into 49 Choice (E) is the correct answer

You may also have to work with a split function—sometimes called a

piecewise function A split function is one that has different definitions,

depending on some condition that is part of the function Here are a couple of examples of split functions:

Functions of this type are fairly self-explanatory It’s just necessary to check the conditions of the function before plugging values in to make sure you’re using the right function definition

DRILL 2: FUNCTIONS USING STANDARD

NOTATION

Practice working with functions in the following questions The answers can be found in Part IV

1 If f(x) =x2 − x3, then f(−1) =

(A) −2 (B) −1 (C) 0 (D) 1 (E) 2

3 If , then how much does f(z) increase as z

(A) 0.64

(B) 1.07

(C) 2.96

(D) 3.84

(E) 5.75

11 If g(t) = t3 + t2 − 9t − 9, then g(3) =

(A) −9

(B) 0

(C) 9

(D) 27

(E) 81

14 If , which of the following is equal to f(3,

−6) ?

(A) −48

(B) −6

(C) 3

(D) 6

(E) 18

15 If h(x) =x2 + x − 2, and h(n) = 10, then n could be which

of the following?

(A) −4

(B) −3

(C) −1

(D) 1

(E) 2

19 The function f is given by f (x) = x • [x], where [x] is

defined to be the greatest factor of x that does not equal

x What is f(75) ?

(A) 25

(B) 225

(C) 625

(D) 1,125

(E) 1,875

20 What is the value of g(−y) if y = 3 ?

(A) −6.0

(B) −3.0

(C) −1.5

(D) 1.5

(E) 6.0

37 f(2,3) + f(0.5,4) =

(A) 6.5

(B) 9.167

(C) 9.5

(D) 10

(E) 13