Which graph has the following properties?

Question

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 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 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.

Answer 1

To determine which graph fits the given properties, let's break down each property:

1. The y-intercept is at (0, 22): This means that when \( x = 0 \), \( y = 22 \).

2. The horizontal asymptote is at \( y = 5 \): This indicates that as \( x \) approaches positive or negative infinity, the value of \( y \) approaches 5.

3. The graph is decreasing for all values of \( x \): This means that as \( x \) increases, \( y \) should continually decrease.

Given these properties, we can analyze the graph descriptions provided.

Analysis of the Options:

1. First Graph:

   • A y-intercept at (0, 22) is not mentioned.
   • No specific details about the horizontal asymptote are provided.
   • It is unclear if the graph is decreasing.

2. Second Graph:

   • Same issues as the first graph, without a specific y-intercept or behavior of the graph.

3. Third Graph:

   • If the solid curve intersects the y-axis at (0, 22), then it meets the y-intercept condition.
   • However, without more information about asymptotes or the direction of the curve, it cannot be concluded to fit all conditions definitively.

4. Fourth Graph:

   • Again, lacks details about a specific y-intercept or asymptotes.

Conclusion:

Considering the properties crucially needed and assuming standard behaviors of rational functions, the third graph references an intersection point on the y-axis (assuming that point is (0, 22) based on common sense). However, without explicit confirmation of a horizontal asymptote, we still can't be certain.

The summary analysis could guide the choice, but technically speaking, the ideal graph would be depicted in clearer terms regarding asymptotes and behavior. Based on the y-intercept stated, the third graph seems the most likely candidate assuming its behavior matches the properties.

Therefore, if the third graph does indeed intersect (0, 22), that would likely be the correct graph based solely on the properties given.