Student Page 2.8.4 Distinguishing Linear from Other Functions
1.
What do you know about linear equations? Give brief answers now and think about these questions as you work on the problems below.
(a)
What patterns would you see in a table of data that can be modeled by a linear equation?
(b)
How can you tell a graph can be modeled by a linear equation?
(c)
What does an equation of a linear equation look like?
(d)
How can you tell a story can be modeled by a linear equation?
2.
Study the data sets. Label each data set as linear or non-linear. Explain your choice.
(a)
| \(x\) | \(y\) |
|---|---|
| \(-5\) | \(-14\) |
| \(-4\) | \(-12\) |
| \(-3\) | \(-10\) |
| \(-2\) | \(-8\) |
| \(-1\) | \(-6\) |
| 0 | \(-4\) |
| 1 | \(-2\) |
| 2 | 0 |
| 3 | 2 |
| 4 | 4 |
| 5 | 6 |
Linear / Non-linear? Explain:
(b)
| \(x\) | \(y\) |
|---|---|
| \(-5\) | 0.03125 |
| \(-4\) | 0.0625 |
| \(-3\) | 0.125 |
| \(-2\) | 0.25 |
| \(-1\) | 0.5 |
| 0 | 1 |
| 1 | 2 |
| 2 | 4 |
| 3 | 8 |
| 4 | 16 |
| 5 | 32 |
Linear / Non-linear? Explain:
(c)
| \(x\) | \(y\) |
|---|---|
| \(-5\) | 25 |
| \(-4\) | 16 |
| \(-3\) | 9 |
| \(-2\) | 4 |
| \(-1\) | 1 |
| 0 | 0 |
| 1 | 1 |
| 2 | 4 |
| 3 | 9 |
| 4 | 16 |
| 5 | 25 |
Linear / Non-linear? Explain:
3.
Categorize each graph as linear or non-linear. Explain your choice.
(a)
Linear / Non-linear? Explain:
(b)
Linear / Non-linear? Explain:
(c)
Linear / Non-linear? Explain:
4.
Gather data for each story. Label each data set as linear or non-linear. Explain your choice.
(a)
Geppetto carved Pinocchio a 2-inch long nose. Each time Pinocchio tells a lie, his nose grows 3 inches. How long will his nose be after 1 lie? 2 lies? 3 lies? \(L\) lies?
| Lie Number | Nose Length in inches |
|---|---|
| 0 | 2 |
| 1 | |
| 2 | |
| 3 | |
| 4 | |
| 5 | |
| \(L\) |
Linear / Non-linear? Explain:
(b)
Geppetto carved Pinocchio a 2-inch long nose. Each time Pinocchio tells a lie, his nose doubles in length. How long will his nose be after 1 lie? 2 lies? 3 lies? \(L\) lies?
| Lie Number | Nose Length in inches |
|---|---|
| 0 | 2 |
| 1 | |
| 2 | |
| 3 | |
| 4 | |
| 5 | |
| \(L\) |
Linear / Non-linear? Explain:
(c)
Geppetto carved Pinocchio a 2-inch long nose. Each time Pinocchio tells a lie, his nose grows from its previous length by the same number of inches as the number of lies he has told. For example, after 1 lie, his nose will be 2 + 1 = 3 inches long. After 2 lies, his nose will be 3 + 2 = 5 inches long. How long will his nose be after 3 lies? 4 lies? 5 lies? \(L\) lies?
| Lie Number | Nose Length in inches |
|---|---|
| 0 | 2 |
| 1 | 3 |
| 2 | 5 |
| 3 | |
| 4 | |
| 5 | |
| \(L\) |
Linear / Non-linear? Explain:
5.
Categorize each equation as linear or non-linear. Explain your choice.
(a)
\(y = 3x + 4\)
Linear / Non-linear? Explain:
(b)
\(y = 2^x + 3\)
Linear / Non-linear? Explain:
(c)
\(y = x^2 + 1\)
Linear / Non-linear? Explain:
6.
Revisit Exercise 2.8.3.1. What can you add to your previous answers? Use more space as needed.
(a)
What patterns would you see in a table that can be modeled by a linear equation?
(b)
How can you tell a graph can be modeled by a linear equation?
(c)
What does an equation of a linear equation look like?
(d)
How can you tell a story can be modeled by a linear equation?