Worksheet for identifying linear, exponential, quadratic, or neither functions with visual examples and explanations.

To solve the problem, we need to determine the type of function (linear, exponential, quadratic, or neither) for each given equation or scenario and then color-code them accordingly. Let's go through each one step by step.

Key Definitions:

1. Linear Function: A function of the form \( y = mx + b \), where \( m \) and \( b \) are constants.
2. Exponential Function: A function of the form \( y = ab^x \), where \( a \) and \( b \) are constants, and \( b > 0 \), \( b \neq 1 \).
3. Quadratic Function: A function of the form \( y = ax^2 + bx + c \), where \( a \), \( b \), and \( c \) are constants, and \( a \neq 0 \).
4. Neither: Any function that does not fit the above categories.

Step-by-Step Analysis:

#### 1. Equations:
1. \( y = 7x + 8 \)
- This is in the form \( y = mx + b \).
- Type: Linear

2. \( 6x + y = 13 \)
- Rearrange to \( y = -6x + 13 \).
- Type: Linear

3. \( y = x^2 + 3x + 2 \)
- This is in the form \( y = ax^2 + bx + c \).
- Type: Quadratic

4. \( y = x^2 + 1 \)
- This is in the form \( y = ax^2 + bx + c \).
- Type: Quadratic

5. \( (-2)x + 3y = 12 \)
- Rearrange to \( y = \frac{2}{3}x + 4 \).
- Type: Linear

6. \( 3x - 7y = 21 \)
- Rearrange to \( y = \frac{3}{7}x - 3 \).
- Type: Linear

7. \( x^2 - 3x + 2 = 0 \)
- This is a quadratic equation, but it is not a function in the form \( y = f(x) \).
- Type: Neither

8. \( x^2 + 10x + 8 = 0 \)
- This is a quadratic equation, but it is not a function in the form \( y = f(x) \).
- Type: Neither

9. \( x^2 = 17 \)
- This is not a function in the form \( y = f(x) \).
- Type: Neither

10. \( f(x) = (x + 2)^2 \)
- Expand to \( f(x) = x^2 + 4x + 4 \).
- Type: Quadratic

11. \( y = 2x + 12 \)
- This is in the form \( y = mx + b \).
- Type: Linear

12. \( y = -3(x - 5) \)
- Expand to \( y = -3x + 15 \).
- Type: Linear

#### 2. Graphs:
1. Graph 1: Straight line
- Type: Linear

2. Graph 2: Parabola
- Type: Quadratic

3. Graph 3: Exponential curve
- Type: Exponential

4. Graph 4: Parabola
- Type: Quadratic

#### 3. Tables:
1. Table 1:
- Points: \((1, 2)\), \((2, 4)\), \((3, 6)\), \((4, 8)\)
- The \( y \)-values increase linearly with \( x \).
- Type: Linear

2. Table 2:
- Points: \((1, 3)\), \((2, 9)\), \((3, 27)\), \((4, 81)\)
- The \( y \)-values increase exponentially with \( x \).
- Type: Exponential

3. Table 3:
- Points: \((1, 2)\), \((2, 5)\), \((3, 10)\), \((4, 17)\)
- The \( y \)-values follow a quadratic pattern.
- Type: Quadratic

4. Table 4:
- Points: \((1, 3)\), \((2, 3)\), \((3, 3)\), \((4, 3)\)
- The \( y \)-values are constant.
- Type: Linear (constant function)

#### 4. Scenarios:
1. Scenario 1: A golf ball is hit at the driving range.
- The path of a golf ball is typically parabolic.
- Type: Quadratic

2. Scenario 2: The carried signal on every cell phone has a half-life of 3 minutes.
- Half-life indicates exponential decay.
- Type: Exponential

3. Scenario 3: The population of bacteria doubles every week.
- Doubling every week indicates exponential growth.
- Type: Exponential

4. Scenario 4: Mr. Green decided to plant 5 seeds in his garden.
- This is a discrete event and does not represent a continuous function.
- Type: Neither

5. Scenario 5: A basketball team won 3 games.
- This is a discrete event and does not represent a continuous function.
- Type: Neither

6. Scenario 6: The flight path of an Angry Bird.
- The path of an Angry Bird is typically parabolic.
- Type: Quadratic

Final Answer:

\[
\boxed{
\begin{array}{c|c}
\text{Equation/Scenario} & \text{Type} \\
\hline
y = 7x + 8 & \text{Linear} \\
6x + y = 13 & \text{Linear} \\
y = x^2 + 3x + 2 & \text{Quadratic} \\
y = x^2 + 1 & \text{Quadratic} \\
(-2)x + 3y = 12 & \text{Linear} \\
3x - 7y = 21 & \text{Linear} \\
x^2 - 3x + 2 = 0 & \text{Neither} \\
x^2 + 10x + 8 = 0 & \text{Neither} \\
x^2 = 17 & \text{Neither} \\
f(x) = (x + 2)^2 & \text{Quadratic} \\
y = 2x + 12 & \text{Linear} \\
y = -3(x - 5) & \text{Linear} \\
\hline
\text{Graph 1} & \text{Linear} \\
\text{Graph 2} & \text{Quadratic} \\
\text{Graph 3} & \text{Exponential} \\
\text{Graph 4} & \text{Quadratic} \\
\hline
\text{Table 1} & \text{Linear} \\
\text{Table 2} & \text{Exponential} \\
\text{Table 3} & \text{Quadratic} \\
\text{Table 4} & \text{Linear} \\
\hline
\text{Scenario 1} & \text{Quadratic} \\
\text{Scenario 2} & \text{Exponential} \\
\text{Scenario 3} & \text{Exponential} \\
\text{Scenario 4} & \text{Neither} \\
\text{Scenario 5} & \text{Neither} \\
\text{Scenario 6} & \text{Quadratic} \\
\end{array}
}
\]