5 Steps to a 5 AP Calculus AB 2019 - William Ma

MA 3972-MA-Book May 8, 2018 13:46

Review of Precalculus 57

4. Check whether the endpoints satisfy the inequality. Since the inequality is less than or
   equal to 1, the endpoint atx=2 is included in the solution.


5. Write the solution to the inequality. The solution is the interval [2, 3).

Example 3

Solve the inequality

1

x

≥xby using a graphing calculator. (See Figure 5.2-6.)

ToolsF1 TraceF3

MAIN RAD AUTO FUNC

ZoomF2 ReGraphF4 MathF5 DrawF6 F7Pen

[−8, 8] by [−4, 4]

Figure 5.2-6

1. Entery 1 =

1

x

andy 2 =x.

2. Find the intersection points:x=−1 andx=1. (Note that atx=0,y 1 is undefined.)


3. Determine the intervals on whichy 1 ≥y 2. The intervals are (−∞,−1) and (0, 1).


4. Check whether the endpoints satisfy the inequality: Since the inequality is greater than
   or equal tox, the endpoints atx=−1 andx=1 are included in the solution.


5. Write the solution to the inequality. The solution is the interval (−∞,−1]∪(0, 1].

5.3 Functions

Main Concepts:Definition of a Function, Operations on Functions, Inverse Functions,

Trigonometric and Inverse Trigonometric Functions, Exponential and

Logarithmic Functions

Definition of a Function

A functionf is a set of ordered pairs (x,y) in which for everyxcoordinate there isone and

only onecorrespondingycoordinate. We writef(x)=y. The domain off is the set of all

possible values ofx, and the range offis the set of all values ofy.

The Vertical Line Test

If all vertical lines pass through the graph of an equation at no more than one point, then

the equation is a function.

Example 1

Giveny=

√

9 −x^2 , sketch the graph of the equation, determine if the equation is a function,

and find the domain and range of the equation. (See Figure 5.3-1.)