Asked by HaydenReturned
Which graph has the following properties?
The y-intercept is at (0,22)
.
The horizontal asymptote is at y=5
.
The graph is decreasing for all values of x.
(1 point)
Responses
A coordinate plane's x-axis ranges from negative 1 to 6 by 1-unit increments and its y-axis ranges from negative 2 to 26 by 2-unit increments. A solid curve and a dotted line with arrows at both ends are plotted.
Image with alt text: A coordinate plane's x-axis ranges from negative 1 to 6 by 1-unit increments and its y-axis ranges from negative 2 to 26 by 2-unit increments. A solid curve and a dotted line with arrows at both ends are plotted.
A coordinate plane's x-axis ranges from negative 1 to 6 by 1-unit increments and its y-axis ranges from negative 2 to 30 by 2-unit increments. A solid curve and a dotted line with arrows at both ends are plotted.
Image with alt text: A coordinate plane's x-axis ranges from negative 1 to 6 by 1-unit increments and its y-axis ranges from negative 2 to 30 by 2-unit increments. A solid curve and a dotted line with arrows at both ends are plotted.
A coordinate plane's x-axis ranges from negative 6 to 1 by 1-unit increments and its y-axis ranges from negative 2 to 26 by 2-unit increments. A solid curve and a dotted line with arrows at both ends are plotted.
Image with alt text: A coordinate plane's x-axis ranges from negative 6 to 1 by 1-unit increments and its y-axis ranges from negative 2 to 26 by 2-unit increments. A solid curve and a dotted line with arrows at both ends are plotted.
A coordinate plane's x-axis ranges from negative 2 to 6 and its y-axis ranges from negative 2 to 24, both by 2-unit increments. A solid curve and a dotted line with arrows at both ends are plotted. The solid curve intersects a point plotted on the y-axis.
The y-intercept is at (0,22)
.
The horizontal asymptote is at y=5
.
The graph is decreasing for all values of x.
(1 point)
Responses
A coordinate plane's x-axis ranges from negative 1 to 6 by 1-unit increments and its y-axis ranges from negative 2 to 26 by 2-unit increments. A solid curve and a dotted line with arrows at both ends are plotted.
Image with alt text: A coordinate plane's x-axis ranges from negative 1 to 6 by 1-unit increments and its y-axis ranges from negative 2 to 26 by 2-unit increments. A solid curve and a dotted line with arrows at both ends are plotted.
A coordinate plane's x-axis ranges from negative 1 to 6 by 1-unit increments and its y-axis ranges from negative 2 to 30 by 2-unit increments. A solid curve and a dotted line with arrows at both ends are plotted.
Image with alt text: A coordinate plane's x-axis ranges from negative 1 to 6 by 1-unit increments and its y-axis ranges from negative 2 to 30 by 2-unit increments. A solid curve and a dotted line with arrows at both ends are plotted.
A coordinate plane's x-axis ranges from negative 6 to 1 by 1-unit increments and its y-axis ranges from negative 2 to 26 by 2-unit increments. A solid curve and a dotted line with arrows at both ends are plotted.
Image with alt text: A coordinate plane's x-axis ranges from negative 6 to 1 by 1-unit increments and its y-axis ranges from negative 2 to 26 by 2-unit increments. A solid curve and a dotted line with arrows at both ends are plotted.
A coordinate plane's x-axis ranges from negative 2 to 6 and its y-axis ranges from negative 2 to 24, both by 2-unit increments. A solid curve and a dotted line with arrows at both ends are plotted. The solid curve intersects a point plotted on the y-axis.
Answers
There are no human answers yet.
Answered by
GPT-4o mini
To find the graph that matches the given properties:
1. **Y-intercept at (0, 22)**: This means that when \( x = 0 \), \( y \) should equal 22.
2. **Horizontal asymptote at \( y = 5 \)**: This indicates that as \( x \) approaches infinity (or negative infinity), the value of \( y \) approaches 5.
3. **Decreasing for all values of \( x \)**: This means the function is always going down as \( x \) increases.
With these properties in mind, we're looking for a graph that meets all three criteria.
### Analysis of Responses:
- **First option**: The y-intercept is (0, 22), and the horizontal asymptote appears to be below this value, potentially seating at y = 5. A decreasing curve fits this description.
- **Second option**: While it's unclear visually, it seems to have the same setup regarding the y-intercept, but we check if the horizontal asymptote exists at y=5.
- **Third option**: The graph may not intersect at y=22 or follow the previously specified conditions.
- **Fourth option**: Again, in this instance, we require a decreasing function and an identifying horizontal asymptote; while it intersects at y=22, the behavior needs confirmation.
### Conclusion
The first response with the y-intercept at (0, 22) and the horizontal asymptote at y=5, along with the description of a completely decreasing function as you move along the x-axis seems to fit.
Thus, the answer is that the **first graph** has the properties stated.
1. **Y-intercept at (0, 22)**: This means that when \( x = 0 \), \( y \) should equal 22.
2. **Horizontal asymptote at \( y = 5 \)**: This indicates that as \( x \) approaches infinity (or negative infinity), the value of \( y \) approaches 5.
3. **Decreasing for all values of \( x \)**: This means the function is always going down as \( x \) increases.
With these properties in mind, we're looking for a graph that meets all three criteria.
### Analysis of Responses:
- **First option**: The y-intercept is (0, 22), and the horizontal asymptote appears to be below this value, potentially seating at y = 5. A decreasing curve fits this description.
- **Second option**: While it's unclear visually, it seems to have the same setup regarding the y-intercept, but we check if the horizontal asymptote exists at y=5.
- **Third option**: The graph may not intersect at y=22 or follow the previously specified conditions.
- **Fourth option**: Again, in this instance, we require a decreasing function and an identifying horizontal asymptote; while it intersects at y=22, the behavior needs confirmation.
### Conclusion
The first response with the y-intercept at (0, 22) and the horizontal asymptote at y=5, along with the description of a completely decreasing function as you move along the x-axis seems to fit.
Thus, the answer is that the **first graph** has the properties stated.
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