Question

Question
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 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.
Image with alt text: 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.

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.
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Answer 1

To determine which graph fits the properties given, we can analyze each of the criteria:

1. **Y-intercept is at (0, 22)** - This means the graph should cross the y-axis at the point where y = 22.

2. **Horizontal asymptote is at y = 5** - This indicates as x approaches either negative or positive infinity, the value of the function approaches 5.

3. **The graph is decreasing for all values of x** - This indicates the curve should consistently slope downwards as we move from left to right.

Now, let's analyze the options:

1. **First Option:**
- The y-axis intercept is not specified in the description.
- We cannot determine the asymptote based on the provided information.
- There is no information suggesting the graph decreases.

2. **Second Option:**
- The description indicates that the solid curve intersects the y-axis but does not specify where it does (could be at 22).
- Asymptote information is not provided.
- No details on whether the graph is decreasing are mentioned.

3. **Third Option:**
- Does not specify the y-intercept.
- Asymptote information is missing.
- No mention of whether the graph is decreasing.

4. **Fourth Option:**
- Again, no specific y-intercept mentioned.
- Asymptote is not referenced.
- It gives no information on whether the graph is decreasing.

Given that none of the options explicitly refer to the properties required in the question (especially the y-intercept of (0, 22) and a horizontal asymptote of y = 5), the question seems to be missing explicit graphical data that would allow us to discern the correct option.

To conclude, based on the properties given, no option definitively meets all criteria. If any option provided clear graphical shapes (e.g., a hyperbola or a rational function) that satisfied the conditions, further graphical analysis would be needed. Please review the graphs visually or clarify further details about their characteristics for better assistance.