﻿ ﻿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 x, f(x) < 0;

2. for some values of x, f(x) = 0;

3. for some values of x, f(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 x that satisfy f(x) = 0.

EXAMPLE

Find the set of values for x that satisfies x2 – 3x – 4 < 0.

Graph y = x2 – 3x – 4. You need to find the x values of points on the graph that lie below the x-axis. First find the zeros: x = 4, x = –1. The points that lie below the x-axis are (strictly) between –1 and 4, or –1 < x < 4.

EXERCISES

1. Which of the following is equivalent to 3x2 x < 2?

(A) (B) (C) (D) (E) 2. Solve x5 – 3x3 + 2x2 – 3 > 0.

(A) (B) (–1.90,–0.87)

(C) (D) (–0.87,1.58)

(E) 3. The number of integers that satisfy the inequality x2 + 48 < 16x is

(A) 0

(B) 4

(C) 7

(D) an infinite number

(E) none of the above

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