Review4

Models of Functions

Notes: 1. Linear function
2. Quadratic function

1. Oil Changes and Engine Repairs

# Oil changes per year	3	5	2	3	1	4	6	4	3	2	0	10	7
Cost of Repairs ($)	300	300	500	400	700	400	100	250	450	650	600	0	150

Analyses:

    a.    How should the axes be labeled to plot the graph of these points?

    b.    Plot the points on a graph. Draw the line that best fits.

    c.    What does the sloping line mean in terms of Cost of repairs?

    d.    Determine the slope of the line. Use proper units to explain what it means.

    e.    Determine the y-intercept. What does it mean here?

    f.    Determine an equation for this relation.

    g.    Determine the x-intercept. What does it mean here?

    h.    How much would repairs cost if there are 4 oil changes per year?

Using the calculator

Graphing from Lists:

Press STAT   select 1:Edit Enter

Enter the data from the table.

Go to 2^nd Y= select 1:Plot 1 Enter On Enter

Move down and select the first Type of graph then Xlist L1, Ylist L2, Mark

Press ZOOM select 9:ZoomStat   Graph appears

You may first want to sort in ascending order by pressing STAT   2:Sort A(L1, L2)

Regression graph that best fits:

STAT move to CALC select 4:LinReg(ax + b) or 5:QuadReg (depending on the shape). Enter

To paste the parameters of the equation:

Press Y= then VARS select 5:Statistics Move to EQ Enter
Press GRAPH

2. Speed vs. Fuel Consumption for the Honda Civic

Table I: Linear Model

Speed

km/h

Consumption

km/L

9.8

10.6

11.3

11.9

12.3

12.9

13.2

13.4

Analyses I:

1. Explain how you calculate consumption in km per litre for a car?

2. According to the table above, at what speed does the Honda Civic get its best fuel consumption?

3. Graph this set of data. What does the graph of these data, look like?

4. What does the shape of the graph mean?

<> 5. Use the calculator to find the equation of this curve.

6. If the trend stays the same, what could be the fuel consumption for a speed of 96 km/h?

Table II: Quadratic Model

Speed

km/h

104

Consumption

km/L

4.2

6.4

9.8

10.6

11.3

11.9

12.3

12.9

13.2

13.4

12.8

12.1

11.5

Analyses II:

1. According to the table above, at what speed does the Honda Civic get its best fuel consumption?

2. Graph this set of data. What does the graph of the data shown, look like?

3. What does the shape of the graph mean?

4. What speed gives the best consumption? Which point of the graph is this?

5. What happens to the consumption beyond this point?

6. Use the calculator to find the equation of this graph.

7. If the trend stays the same, what could be the fuel consumption for a speed of 112 km/h?

3. Maximum Area of Rectangle

Problem:

        You are given 18 metres of fencing to create a rectangular pen for
        your dog.
        Which dimensions of the rectangle would produce the largest area
        for the pen?

Complete the table with values of width and related length and area.

Width (m)	Length (m)	Area (m)
1.0
2.0

Analyses:

1.    Could the width be larger than 9 m? Explain why or why not.

2.    How does the perimeter of the pen change, as the width goes from 0 m to 9 m?

3.    Plot area for the different values of width, what is the shape of the graph?

4.    Maximum area of the pen:

      a.    What dimensions does the pen have when its area is biggest?

b.    What is the shape of the pen in this case?

5.    What point on the graph represents the width that produces

       a.    the maximum area?

       b.    the minimum area?

6.    Choose two points on the graph that have the same area.

       a.    What do you notice about the values of length and width for these points?

       b.   How are these rectangles similar? How are they different?

7.    Determine an equation for this graph.

8.    Suppose you were given an extra 7 m of fencing so you now have 25 m in total.
       What dimensions would result in the largest area for the pen? Explain.

9.    If you had a total of 30 m of fencing, what dimensions would result in the largest area for the pen? Explain.