## SAT SUBJECT TEST MATH LEVEL 2

## PART 2

## REVIEW OF MAJOR TOPICS

## CHAPTER 1

Functions

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1.1 Overview

### Answers and Explanations

Definitions

1. **(A)** Either (3,2) or (3,1), which is not an answer choice, must be removed so that 3 will be paired with only one number.

2. **(E)** For each value of *x *there is only one value

for *y *in each case. Therefore, *f, g, *and *h *are all functions.

3. **(C)** Since division by zero is forbidden, *x *cannot equal 2.

Combining Functions

1. **(E)** *f*(–2) = 3(–2)^{2 }– 2(–2) + 4 = 20.

2. **(D)** *g*(2) = 3^{2} = 9. *f(g*(2)) = *f*(9) = 31.

3. **(C)** To get from *f(x*) to *f(g(x*)), *x*^{2} must become 4*x*^{2}. Therefore, the answer must contain 2*x *since (2*x*)^{2 }= 4*x*^{2}.

4. **(D)** *g(x*) cannot equal 0. Therefore, .

5. **(A)** Since *f*(2) implies that *x *= 2, *g(f*(2)) = 2. Therefore, *g(f*(2)) = 3(*f*(2)) + 2 = 2. Therefore, *f*(2) = 0.

6. **(C)** *p(a*) = 0 implies 4*a *– 6 = 0, so .

* 7. **(E)**

Inverses

1. **(E)** If *y *= 2*x *– 3, the inverse is *x *= 2*y *– 3, which is equivalent to .

2. **(A)** By definition.

3. **(B)** The inverse is {(2,1),(3,2),(4,3),(1,4),(2,5)}, which is not a function because of (2,1) and (2,5). Therefore, the domain of the original function must lose either 1 or 5.

4. **(E)** If this line were reflected about the line *y = x *to get its inverse, the slope would be less than 1 and the *y*-intercept would be less than zero. The only possibilities are Choices D and E. Choice D can be excluded because since the *x*-intercept of *f(x*) is greater than –1, the *y*-intercept of its inverse must be greater than –1.

Odd and Even Functions

1. **(D)** Use the appropriate test for determining whether a relation is even.

I. The graph of *y *= 2 is a horizontal line, which is symmetric about the *y*-axis, so *y *= 2 is even.

II. Since *f*(–*x*) = –*x * *x *= *f(x*) unless *x *= 0, this function is not even.

III. Since (–*x*)^{2 }+ *y*^{2} = 1 whenever *x*^{2} + *y*^{2} = 1, this relation is even.

2. **(D)** Use the appropriate test for determining whether a relation is odd.

I. The graph of *y *= 2 is a horizontal line, which is not symmetric about the origin, so *y *= 2 is not odd.

II. Since *f*(–*x*) = –*x *= –*f(x*), this function is odd.

III. Since (–*x*)^{2} + (–*y*)^{2} = 1 whenever *x*^{2} + *y*^{2} = 1, this relation is odd.

3. **(B)** The analysis of relation III in the above examples indicates that I and II are both even and odd. Since –*x *+ *y * 0 when *x *+ *y *= 0 unless *x *= 0, III is not even, and is therefore not both even and odd.

4. **(C)** A is even, B is odd, D is even, and E is odd. C is not even because (–*x*)^{3 }– 1 = –*x*^{3} – 1, which is neither *x*^{3} – 1 nor –*x*^{3} + 1.