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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 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.
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 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.

1 answer

To determine which graph fits the given properties, let's analyze each condition:

  1. Y-Intercept at (0, 22): This means that when \( x = 0 \), \( y \) must equal 22.

  2. Horizontal Asymptote at \( y = 5 \): This implies that as \( x \) approaches positive or negative infinity, the graph should approach the line \( y = 5 \).

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

Given these conditions, let's analyze the options:

  1. First Graph: Since we cannot see the actual graphs, we would need to rely on the descriptions provided. However, there is no mention of the y-intercept in the description, making it hard to verify if it intersects at (0, 22).

  2. Second Graph: Similar to the first, the description does not mention the specific y-intercept.

  3. Third Graph: Again, the y-intercept is not specifically stated in this description.

  4. Fourth Graph: Like the others, the description lacks mention of the y-intercept.

Since none of the options specifically provide a clear y-intercept of (0, 22), and without being able to visualize the actual graphs, we cannot definitively determine which graph meets all three conditions.

Based purely on deductive reasoning from the given conditions, a rational choice would suggest looking for significant trends in the graphs that can display such characteristics: a high y-intercept, a clear declining trend, and a horizontal line at \( y = 5 \) as \( x \) progresses.

If the focus is on graphical aspects, ensure to closely examine the visible markers for the y-intercept (227) and the behavior as \( x \) increases.