﻿ INEQUALITIES - Polynomial Functions - Functions - REVIEW OF MAJOR TOPICS - SAT SUBJECT TEST MATH LEVEL 2 ﻿

## PART 2 ## REVIEW OF MAJOR TOPICS ## CHAPTER 1Functions

### 1.2 Polynomial Functions ### INEQUALITIES

Given any algebraic expression f(x), there are exactly three situations that can exist:

1. for some values of xf(x) < 0;

2. for some values of xf(x) = 0;

3. for some values of xf(x) > 0.

If all three of these sets of numbers are indicated on a number line, the set of values that satisfy f(x) < 0 is always separated from the set of values that satisfy f(x) > 0 by the values of that satisfy f(x) = 0.

EXAMPLE

Find the set of values for that satisfies x– 3– 4 < 0.

Graph x– 3– 4. You need to find the values of points on the graph that lie below the x-axis. First find the zeros: = 4, = –1. The points that lie below the x-axis are (strictly) between –1 and 4, or –1 < < 4.

EXERCISES

1.       Which of the following is equivalent to 3x– < 2?

(A) (B) (C) (D) (E) 2.       Solve x5 – 3x+ 2x– 3 > 0.

(A) (B)  (–1.90,–0.87)

(C) (D)  (–0.87,1.58)

(E) 3.       The number of integers that satisfy the inequality x+ 48 < 16is

(A)  0

(B)  4

(C)  7

(D)  an infinite number

(E)  none of the above

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