5. Graph the function. State the domain, range, and asymptote, Label two points. y = 5(13)x Parent points: (0,5) and (5) an Domain: All real numbers -2.5
5. Graph the function. State the domain, range, and asymptote, Label two points. y = 5(13)x Parent points: (0,5) and (5) an Domain: All real numbers -2.5
Chapter2: Functions And Their Graphs
Section2.4: A Library Of Parent Functions
Problem 47E: During a nine-hour snowstorm, it snows at a rate of 1 inch per hour for the first 2 hours, at a rate...
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![**Graph the Function**
### Function
\[ y = 5 \left(\frac{1}{3}\right)^x \]
### Domain and Range
- **Domain**: All real numbers
- **Range**: y > 0 (the graph never touches the x-axis but comes infinitely close, indicating that the value of \( y \) is always positive)
### Asymptote
- **Horizontal Asymptote**: y = 0
### Labeled Points
The graph includes the following points:
- \( (0, 5) \)
- \( (1, \frac{5}{3}) \)
These points are plotted on a Cartesian plane.
### Graph Explanation
The given image displays a Cartesian grid with the function \( y = 5 \left(\frac{1}{3}\right)^x \) plotted. This function represents an exponential decay curve. Below are key points of the graph:
1. **Intercepts**:
- The graph crosses the y-axis at point \( (0, 5) \), which is the y-intercept.
2. **Behavior**:
- As \( x \) increases, \( y \) decreases rapidly towards 0 but never reaches it, showcasing the horizontal asymptote at y = 0.
- As \( x \) decreases, \( y \) increases without bound.
3. **Appearance**:
- The curve starts from the y-intercept at \( (0, 5) \) and moves downward as it extends to the right along the x-axis.
- There are marked points at \( (0, 5) \) and \( (1, \frac{5}{3}) \) for clarification and reference.
This exercise is an example of graphing exponential functions and understanding their properties, such as domain, range, and asymptotes.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F76555388-6a8d-4d01-aabe-a551666898f4%2Fa2f627a0-960b-4787-beb9-7fc609912fc7%2Fozobnjc_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Graph the Function**
### Function
\[ y = 5 \left(\frac{1}{3}\right)^x \]
### Domain and Range
- **Domain**: All real numbers
- **Range**: y > 0 (the graph never touches the x-axis but comes infinitely close, indicating that the value of \( y \) is always positive)
### Asymptote
- **Horizontal Asymptote**: y = 0
### Labeled Points
The graph includes the following points:
- \( (0, 5) \)
- \( (1, \frac{5}{3}) \)
These points are plotted on a Cartesian plane.
### Graph Explanation
The given image displays a Cartesian grid with the function \( y = 5 \left(\frac{1}{3}\right)^x \) plotted. This function represents an exponential decay curve. Below are key points of the graph:
1. **Intercepts**:
- The graph crosses the y-axis at point \( (0, 5) \), which is the y-intercept.
2. **Behavior**:
- As \( x \) increases, \( y \) decreases rapidly towards 0 but never reaches it, showcasing the horizontal asymptote at y = 0.
- As \( x \) decreases, \( y \) increases without bound.
3. **Appearance**:
- The curve starts from the y-intercept at \( (0, 5) \) and moves downward as it extends to the right along the x-axis.
- There are marked points at \( (0, 5) \) and \( (1, \frac{5}{3}) \) for clarification and reference.
This exercise is an example of graphing exponential functions and understanding their properties, such as domain, range, and asymptotes.
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