Activity 1 - 9

Fund-Raiser Revisited

5-Minute Check on Activity 1-85-Minute Check on Activity 1-85-Minute Check on Activity 1-85-Minute Check on Activity 1-8

Click the mouse button or press the Space Bar to display the answers.Click the mouse button or press the Space Bar to display the answers.

1. In a wind chill chart, what are the independent variables?

2. In a wind chill chart, what is the dependent variable?

3. How do we test a graph to see if it is a function?

4. What is the domain and range of x +2 ?

5. What is the domain and range of ?

Wind-speed and temperature

1----------

x - 3

Apparent temperature

Vertical line test

Domain: x > -2 Range: y > 0

Domain: x ≠ 3

Range: y ≠ 0 (graph it! we will see just how this works later)

Objectives

• Solve an equation numerically

• Solve an equation graphically

• Distinguish between a situation represented by a graph of distinct points versus a continuous path

Vocabulary• Evaluated – plugging in a value for the variable

• Equation – two numerical expressions separated by an =

• Numerical method – guess a number, check and repeat

• Graphical method – plot points and interpolate the graph

• Solution – a replacement value for the variable that produces equal numerical values on both sides of the equation

• Continuous – a graph is continuous if there are no gaps, or jumps in the graph

• Discontinuity – a jump, gap or disconnect between two points on the graph

Activity

In a previous activity we found the equation y = 2.5x modeled the fund raiser with x representing the number of tickets sold and y representing the amount of money donated to summer camp fund.

a)How much money is raised if 84 tickets are sold?

b)Fill in the table below

# of Tickets Sold Amount Raised

26

94

278

Activity - 1

In a previous activity we found the equation y = 2.5x modeled the fund raiser with x representing the number of tickets sold and y representing the amount of money donated to summer camp fund.

a)Use the table below to guess at how many tickets have to be sold to raise $200

b)What’s the disadvantage to “guess & check”?

# of Tickets Sold Amount Raised

100 250

Activity - 2

In a previous activity we found the equation y = 2.5x modeled the fund raiser with x representing the number of tickets sold and y representing the amount of money donated to summer camp fund.

a)Use the graph below to determine how many tickets have to be sold to raise $200

b)What’s the disadvantage to a graphical method?

y

x

Problem - 1

The recommended weight of an adult male can be approximated by the formula, w = 5.5 h – 220, where w is recommended weight and h is height in inches.

a)What is the practical domain for the weight function?

b)Complete the following table

c)Graph your values in b).

Ht 60 64 68 72 76 80

W

y

x

Problem - 2

The recommended weight of an adult male can be approximated by the formula, w = 5.5 h – 220 , where w is recommended weight and h is height in inches.

a)Write an equation that can be used to determine the height of a man who weighs 165 pounds.

b)Solve the equation by guess and check

c)Solve the equation by graphing

y

x

Continuous vs Not Continuous

Which of the graphs below are continuous functions and which are not?

y

x

y

x

y

x

Continuous Function

Not Continuous Function

Continuous, but Not a Function

Graphical Continuity

• A graph is continuous if we can graph the entire “curve” without lifting our pencil from the paper.

• There are 3 types of discontinuities– point: where a point is missing in the curve– infinite: where the function is undefined

(denominator equal to zero!)– jump: where we have to jump to the next point on

the graph

Definition: A function is continuous at a number a if

Note: that the definition implicitly requires three things of the function

1. f(a) is defined (i.e., a is in the domain of f)

2.

3.

Note the graphs of the examples of discontinuities below:

lim f(x) = f(a) xa

lim f(x) = f(a) xa

lim f(x) exisits xa

Jump

f(x) = [[x]]

Point

x² - x - 2f(x) = -------------- x - 2

Infinite

1/x if x ≠ 0f(x) = 0 if x = 0

Point

x²/x if x ≠ 0f(x) = 1 if x = 0

Continuity

Summary and Homework

• Summary– To solve an equation using a:• numerical approach: use a guess, check and

repeat process• graphical approach: read the appropriate x,y

coordinates on the graph of the equation• algebra: solve for the variable in question

– Graphs are continuous if you can trace the graph without having to lift your pencil from the paper (no breaks!)

• Homework– pg 83-86; 1-4