Warm-up 12/14/12

1. Solve the system by any method

2. Set up the system of equationsA math test is to have 20 questions. The test format uses multiple choice worth 5 points each and problem solving worth 6 points each. The test has a total of 100 points.

3 8 5

2 2 18

x y

x y

Unit 3: Linears and Exponentials

Function Notation, Combination of Functions

Characteristics of FunctionsProperties: Domain and Range,

Increasing and Decreasing, Intercepts, Asymptotes

Rate of ChangeSequencesTransformationsComparing Sequences and FunctionsGrowth and Decay Models

Key Ideas

04/20/23 Example 1 Are these Functions? If no, WHY NOT?

Input Output

-2 2

1 4

5 6

YES NO

Example 2

2

If f(x) = 2x2 + 3x -7, find f(-3)

Example 3

Given the functions

f(x) = 2x2 + 3x - 7 g(x) = x2 - 5x + 6

Find g(x) – f(x)

-x2 – 8x + 13

Domain:

Range:

x-int:

y-int:

Increasing or Decreasing

Example 4

-10 -8 -6 -4 -2 2 4 6 8 10

-10

-8

-6

-4

-2

2

4

6

8

10

Domain:

Range:

Asymptote:

Rate of Change [-2,0]:

Increasing or Decreasing

Example 5

( , )

( ,5)

5y3

2

Calculate the rate of change from,

(2, 5) to (0, 9).

2

Example 6

Write the formula of the following sequences...

5, -2, -9, -16,… 2, 8, 32, 128,…

12 4

n

na

Example 7

7 12na n

Describe the transformations.

f(x) = -(2)x+4 - 1

Example 8

• Reflect over the x-axis

• Left 4• Down 1

Growth

15%

200

611.80

Given the equation

a)Growth or Decay? ____________

b)What is the rate of growth or decay?

_______

c)What is the initial value? _________

d)Evaluate for x = 8 _________

Example 9

200(1.15)xy

You purchase a car for $24,000. The value of

the car decreases 6% each year.

Write an exponential equation describing the

situation.

What will the car be worth in 12 years?

Example 10

y = 24,000(.94)t

$11,422.09

Coach Riggins is getting the Lax team ready for the upcoming

season. For conditioning he has developed 2 plans:

Plan A: The team starts with 1 mile and increases a quarter of a

mile each day.

Plan B: The team starts with half a mile and it doubles every day for

the first week.

Write the equation for each plan.

Compare the Rate of Change, y-intercept for each.

Example 11

.25 1 y x

.5(2) xy

CW/HW

Mid-Term Unit #3 Review