Warm up1.a. Write the explicit formula for the following sequence -2, 3, 8, 13,… b. Find a10

2.a. Write the recursive formula for the following sequence 2, 8, 14, 20, …

b. Find the 40th term.

The graph below represents Maria’s distance from home one day as she rode her bike to meet friends and do a couple of errands for her mom before returning home.

1. What do the horizontal lines on the graph represent?2. Where in the graph shows her taking care of the 2

errands?

3. Compare how she traveled at the beginning to how she traveled at the very end.

4. Create Maria’s story so that it matches the graph.

Characteristics of Functions

Intercepts• x-intercept – the point at which the

line intersects the x-axis at (x, 0)

• y-intercept – the point at which the line intersects the y-axis at (0, y)

Find the x and y intercepts, then graph.

-3x + 2y = 12

Find the x and y intercepts, then graph.

4x - 5y = 20

Increasing, Decreasing, or Constant

• Sweep from left to right and notice what happens to the y-values

• Finger Test- as you move your finger from left to right is it going up or down?

• Increasing goes up (L to R)• Decreasing falls down (L to R)• Constant is a horizontal graph

Continuous vs Discrete

• Continuous has NO breaks

• Discrete has gaps or breaks

Extrema

•Maximum Point – greatest value of the function

•Minimum Point – least value of the function

Domain & Range

• Domain – all x-values of a function

• Range – all y-values of a function

Notation• Interval – represents an interval

as a pair of numbers. The numbers are the endpoints of the interval. Parentheses and/or brackets are used to show whether the endpoints are excluded or included• Set – using inequalities to describe

the values

Characteristics1. Domain:

2. Range:3. Intercepts:4. Increasing

or Decreasing?

5. Maximum or Minimum?

Average Rate of Change

Rate of Change

• Ratio describing how one quantity changes as another quantity changes

• Slope can be used to describe it

Rate of Change

• Positive – increases over time

• Negative – decreases over time

Rate of Change

• Linear functions have a constant rate of change, meaning values increase or decrease at the SAME rate over a period of time

Rate of Change

• Horizontal lines have 0 rate of change

• Vertical lines have undefined rate of change

Average Rate of Changeusing function notation

2 1

2

2

1

1

2 1

( ) ( )y ym becomes

x x

f x f x

x x

Ex 1 Find the Average Rate of Change

f(x) = 2x – 3 from [2, 4].

2 1

2 1

( ) ( ) (4) (2)

4 2

f x f x f f

x x

5 1

4 2

2

4

2

f(x) = -4x + 10 from [-1, 3].

m = -4

Ex 2 Find the Average Rate of Change

A. Find the rate of change from day 1 to 2.

m = 11

Ex 3 Find the Average Rate of Change

Days (x) Amount of Bacteria f(x)

1 19

2 30

3 48

4 76

5 121

6 192

B. Find the rate of change from day 2 to 5.

9130.3

3

In 2008, about 66 million U.S. households had both landline phones & cell phones. Find the rate of change from 2008 – 2011.

m = -5

Ex 4 Find the Average Rate of Change

Year (x) Households in Millions f(x)

2008 66

2009 61

2010 56

2011 51

51 66

2011 2008

What does this mean?It decreased 5 million households per year from 2008 – 11.

Classwork

Characteristics of Functions

Homework

Rate of Change