Worksheet on identifying exponential functions, including growth, decay, and asymptotes.

Problem Overview:

The task involves analyzing graphs of exponential functions to determine whether they represent growth or decay, identifying the y-intercept, and determining the asymptote. Each graph is labeled with a number, and we need to fill in the blanks for each graph.

Key Concepts:

1. Exponential Growth vs. Decay:
- Growth: The function increases as \( x \) increases. The base of the exponential function is greater than 1.
- Decay: The function decreases as \( x \) increases. The base of the exponential function is between 0 and 1.

2. Y-Intercept:
- The y-intercept is the point where the graph crosses the y-axis (i.e., when \( x = 0 \)).

3. Asymptote:
- For exponential functions, the horizontal asymptote is the value that the function approaches as \( x \) goes to positive or negative infinity. Typically, this is the line \( y = c \) in the general form \( f(x) = a \cdot b^x + c \).

Solution:

#### Graph 1:
- Growth/Decay: The graph shows an increasing trend as \( x \) increases, so it represents Growth.
- Y-Intercept: The graph crosses the y-axis at \( y = 1 \). Thus, the y-intercept is \( (0, 1) \).
- Asymptote: The graph approaches the line \( y = 0 \) as \( x \) decreases. Therefore, the asymptote is \( y = 0 \).

#### Graph 2:
- Growth/Decay: The graph shows an increasing trend as \( x \) increases, so it represents Growth.
- Y-Intercept: The graph crosses the y-axis at \( y = -2 \). Thus, the y-intercept is \( (0, -2) \).
- Asymptote: The graph approaches the line \( y = -3 \) as \( x \) decreases. Therefore, the asymptote is \( y = -3 \).

#### Graph 3:
- Growth/Decay: The graph shows a decreasing trend as \( x \) increases, so it represents Decay.
- Y-Intercept: The graph crosses the y-axis at \( y = 3 \). Thus, the y-intercept is \( (0, 3) \).
- Asymptote: The graph approaches the line \( y = 2 \) as \( x \) increases. Therefore, the asymptote is \( y = 2 \).

#### Graph 4:
- Growth/Decay: The graph shows a decreasing trend as \( x \) increases, so it represents Decay.
- Y-Intercept: The graph crosses the y-axis at \( y = -2 \). Thus, the y-intercept is \( (0, -2) \).
- Asymptote: The graph approaches the line \( y = -1 \) as \( x \) increases. Therefore, the asymptote is \( y = -1 \).

#### Graph 5:
- Growth/Decay: The graph shows a decreasing trend as \( x \) increases, so it represents Decay.
- Y-Intercept: The graph crosses the y-axis at \( y = 0 \). Thus, the y-intercept is \( (0, 0) \).
- Asymptote: The graph approaches the line \( y = -1 \) as \( x \) increases. Therefore, the asymptote is \( y = -1 \).

#### Graph 6:
- Growth/Decay: The graph shows a decreasing trend as \( x \) increases, so it represents Decay.
- Y-Intercept: The graph crosses the y-axis at \( y = -1 \). Thus, the y-intercept is \( (0, -1) \).
- Asymptote: The graph approaches the line \( y = 2 \) as \( x \) increases. Therefore, the asymptote is \( y = 2 \).

#### Graph 7:
- Growth/Decay: The graph shows an increasing trend as \( x \) increases, so it represents Growth.
- Y-Intercept: The graph crosses the y-axis at \( y = 0 \). Thus, the y-intercept is \( (0, 0) \).
- Asymptote: The graph approaches the line \( y = -1 \) as \( x \) decreases. Therefore, the asymptote is \( y = -1 \).

#### Graph 8:
- Growth/Decay: The graph shows a decreasing trend as \( x \) increases, so it represents Decay.
- Y-Intercept: The graph crosses the y-axis at \( y = 2 \). Thus, the y-intercept is \( (0, 2) \).
- Asymptote: The graph approaches the line \( y = 1 \) as \( x \) increases. Therefore, the asymptote is \( y = 1 \).

#### Graph 9:
- Growth/Decay: The graph shows an increasing trend as \( x \) increases, so it represents Growth.
- Y-Intercept: The graph crosses the y-axis at \( y = 0.5 \). Thus, the y-intercept is \( (0, 0.5) \).
- Asymptote: The graph approaches the line \( y = 4 \) as \( x \) decreases. Therefore, the asymptote is \( y = 4 \).

Final Answers:

1. Growth, y-intercept: \( (0, 1) \), Asymptote: \( y = 0 \)
2. Growth, y-intercept: \( (0, -2) \), Asymptote: \( y = -3 \)
3. Decay, y-intercept: \( (0, 3) \), Asymptote: \( y = 2 \)
4. Decay, y-intercept: \( (0, -2) \), Asymptote: \( y = -1 \)
5. Decay, y-intercept: \( (0, 0) \), Asymptote: \( y = -1 \)
6. Decay, y-intercept: \( (0, -1) \), Asymptote: \( y = 2 \)
7. Growth, y-intercept: \( (0, 0) \), Asymptote: \( y = -1 \)
8. Decay, y-intercept: \( (0, 2) \), Asymptote: \( y = 1 \)
9. Growth, y-intercept: \( (0, 0.5) \), Asymptote: \( y = 4 \)

\[
\boxed{
\begin{array}{ccc}
1. & \text{Growth}, & y\text{-intercept: } (0, 1), & \text{Asymptote: } y = 0 \\
2. & \text{Growth}, & y\text{-intercept: } (0, -2), & \text{Asymptote: } y = -3 \\
3. & \text{Decay}, & y\text{-intercept: } (0, 3), & \text{Asymptote: } y = 2 \\
4. & \text{Decay}, & y\text{-intercept: } (0, -2), & \text{Asymptote: } y = -1 \\
5. & \text{Decay}, & y\text{-intercept: } (0, 0), & \text{Asymptote: } y = -1 \\
6. & \text{Decay}, & y\text{-intercept: } (0, -1), & \text{Asymptote: } y = 2 \\
7. & \text{Growth}, & y\text{-intercept: } (0, 0), & \text{Asymptote: } y = -1 \\
8. & \text{Decay}, & y\text{-intercept: } (0, 2), & \text{Asymptote: } y = 1 \\
9. & \text{Growth}, & y\text{-intercept: } (0, 0.5), & \text{Asymptote: } y = 4 \\
\end{array}
}
\]