Assignment: Linear Relationships

Name:______Math 3311

Assignment: Linear relationships

1. Calculate the first difference in x and y, then write the linear equation:

Change in x / x / f(x) / Change in y
/ -6 / --3 /
-3 / 2
0 / 7
3 / 12
6 / 17
9 / 22
12 / 27

Your slope:

Your equation:

2. Calculate the first difference in x and y, then write the linear equation:

Change in x / x / f(x) / Change in y
/ -4 / -45/7 /
-2 / -33/7
0 / -3
2 / -9/7
4 / 3/7
6 / 15/7
8 / 27/7

Your slope:

Your equation:

3. Is the relation of this data linear? If so, write an equation modeling the relationship.

Change in x / x / f(x) / Change in f(x)
/ 0 / 1.44 /
2 / 3.34
7 / 8.09
10 / 10.94

***Since the change in x is not uniform, do you think you need to compute the slope on each interval?

4. Is the relation of this data linear? If so, write an equation modeling the relationship.

Change in x / Altitude
x, thousands of feet / Temperature,
f(x) / Change in f(x)
/ 8 / 197.6 /
4.5 / 203.9
3 / 206.6
2.5 / 207.5

5. A recursive function defines a function by referring to the value of the function at previous whole numbers (the domain is always whole numbers). Consider the recursive function with .

Determine whether the function is linear on its domain. If so, write an algebraic expression for f(n) as a function of n.

Name:______Math 3311

Assignment: Quadratic and cubic relationships

Use first, second, and third differences to determine whether the function is linear, quadratic, or cubic.

Write the equation describing the function.

1.

2.

3.

4.

5. Calculate the first and second differences.

Is the relation quadratic? Explain your answer.

x / f(x) / First Difference / Second Difference
3 / 2
7 / 6
10 / 12
14 / 20
17 / 30

7. Write an equation for a quadratic function having uniform second differences of 6 and passing through the point (1,5).

8. Write an equation for a cubic function having uniform third differences of 1 and passing through the point

9. The table below shows the annual sales of a small corporation over a period of years:

Year / Sales
2006 / $513,000
2007 / $516,000
2008 / $521,000
2009 / $528,000
2010 / $537,000

A. Write a function to model the data.

B. In what year will sales increase $17,000 from the previous year?

Name:______Math 3311

Assignment: Exponential and logarithmic relationships

Determine whether the relation is linear, quadratic, cubic, exponential, or logarithmic. Write the equation.

1.

2.

3.

x / f(x) / First Difference / Second Difference / Third Difference
0 / 600 / /
10 / 480
20 / 384 /
30 / 307.2
40 / 245.76

Your function:

4. Determine whether the relation is linear, quadratic, cubic, exponential, or logarithmic. Write the equation.

x / f(x) / First Difference / Second Difference / Third Difference
-2 / .75 / /
0 / 3
2 / 12 /
4 / 48
6 / 192

Your equation:

5. Determine whether the relation is linear, quadratic, cubic, exponential, or logarithmic. Write the equation.

x / f(x) / First Difference / Second Difference / Third Difference
1 / 1 / /
3 / 3
9 / 5 /
27 / 7
81 / 9

Your equation:

6. Determine whether the relation is linear, quadratic, cubic, exponential, or logarithmic. Write the equation.

x / f(x) / First Difference / Second Difference / Third Difference
1 / 5 / /
4 / 6
16 / 7 /
32 / 7.5
64 / 8

Your equation:

7. Determine whether the relation is linear, quadratic, cubic, exponential, or logarithmic. Write the equation.

x / f(x) / First Difference / Second Difference / Third Difference
0 / 5 / /
1 / 10
2 / 20 /
3 / 40
4 / 80

Your equation:

8 .Determine whether the relation is linear, quadratic, cubic, exponential, or logarithmic. Write the equation.

x / f(x) / First Difference / Second Difference / Third Difference
-1 / .04 / /
1 / 1
3 / 25 /
5 / 625
7 / 15625

Your equation:

9.

A) Complete the table so the relation is a linear function:

x / 0 / 1 / 2 / 3 / 4
f(x) / 3 / 6

B) Complete the table so the relation is a quadratic function:

x / 0 / 1 / 2 / 3 / 4
f(x) / 3 / 6

C) Complete the table so the relation is an exponential function:

x / 0 / 1 / 2 / 3 / 4
f(x) / 3 / 6

For which of the above types of functions (linear, quadratic, exponential) is there more than one correct way to complete the table??? Explain.