Calculus Chapter2

2 - 1 2012 Pearson Education, Inc.. All rights reserved.

2.1 Properties of Functions


Figure 2


Figure 4

Is this a function?


Vertical Line test

Do the following graphs represent functions?


Figure 5a - 5b


Figure 5c - 5d


Your Turn 1

Find the domain and range for the function

2

1.

4y

x


Your Turn 2

Given the function

Find all values of x such that

Solution: Set f (x) equal to 5 and then add 5 to both sides to

make one side equal to 0.

2( ) 2 3 4,f x x x

( ) 5.f x


Even and odd functions

HW pg 53 1, 21-31, 57-61 odd

If f is defined on a symmetric domain, and if f(-x)=f(x), f is even, and if f(-x)=-f(x), f is odd.


2.2 Quadratic Functions


Figure 14


Figure 15


Figure 16


Figure 17


Figure 18


For the function (a) find the y-intercept, (b) find the x intercepts, (c) find the vertex, and (d) sketch the graph.

22 6 1y x x


Your Turn 1 continued


Figure 21-22


Figure 23-25


Figure 28 - 30


Figure 31


Examples

Sketch the graph of the following function indicating its x

and y intercepts if they exist, and find its domain and range.

y=3- 1

y= 9 2


Figure 32

HOMEWORK pg 64, 3-7, 13-19, 35,37, 49-53 odd


2.3 Polynomial and Rational Functions


Figure 33


Figure 34


Your Turn 1

Graph

Solution: Using the principles

of translation and reflection,

we recognize that this is

similar to the graph of

but reflected vertically

(because of the negative in

front of x6 ) and 64 units up.

6( ) 64 .f x x

6 ,y x


Figure 40


Figure 42


Figure 43


Figure 44

HW pg 73 3,5, 27-35, odd 47


2.4 Exponential Functions


Figure 46


Figure 47


Solve /2 325 125 .x x


Your Turn 2

Find the interest earned on $4400 at 3.25% interest compounded

quarterly for 5 years.

Solution: Use the formula for compound interest with P = 4400,

r = 0.0325, m = 4, and t = 5.

The investment plus the interest is $5172.97. The interest

amounts to $5172.97 $4400 = $772.97.

1

tmr

A Pm

5(4)

0.03254400 1

4A

5172.97 Use a calcula tor.


Figure 50

Different exponential curves.


Examples


and y intercepts if they exist, horizontal and vertical

asymptotes if they exist, and find its domain and range.

y=2-

y=+3


Your Turn 3

Find the amount after 4 years if $800 is invested in an account

earning 3.15% compounded continuously.

Solution: In the formula for continuous compounding,

let P = 800, t = 4 and r = 0.0315 to get

or $907.43.

rtA Pe

0.0315(4)800A e

907.43,

HW pg 86 13-31, odd, 37,39, 43


2.5 Logarithmic Functions


Example 1


Figure 54


Your Turn 3

Write the expression

as a sum, difference, or product of simpler logarithms.

2 3log ( / )a x y


Figure 55


Your Turn 4

Evaluate 3log 50.

Use a calcu

3.

la

561

.

.

tor


Your Turn 5

1. Solve for x:

Solution x = 4 and x = 2.

Notice that x = 4 is not a valid value for x in the original

equation, since the logarithm of a negative number is

undefined. The only solution is, therefore, x = 2.

2. Solve for x:

2 2log log ( 2) 3.x x

12 3 .x x

HW pg 98 13-25 odd, 31, 41-47 odd, 75, 77


Graphs of Basic Functions

HOMEWORK pg 107 7-15, 19, 21, 27, 29, 37 REVIEW pg 113 1-18


Examples


and y intercepts if they exist, horizontal and vertical

asymptotes if they exist, and find its domain and range.

y=1-ln(x-2)

y=ln(x+3)-4

Calculus Chapter2

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