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 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.

Answer 1

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.