Question
Which graph has the following properties?
1. The y-intercept is at (0,6)
.
2. The horizontal asymptote is at y=1
.
3. The graph is decreasing for all values of x.
(1 point)
Responses
A coordinate plane's x-axis ranges from negative 1 to 8 and its y-axis ranges from negative 1 to 8, both by 1-unit increments. A solid curve and a dotted line with arrows at both ends are plotted. The solid curve passes through a plotted point.
Image with alt text: A coordinate plane's x-axis ranges from negative 1 to 8 and its y-axis ranges from negative 1 to 8, both by 1-unit increments. A solid curve and a dotted line with arrows at both ends are plotted. The solid curve passes through a plotted point.
A coordinate plane's x-axis ranges from negative 1 to 6 and its y-axis ranges from negative 1 to 8, both by 1-unit increments. A solid curve and a dotted line with arrows at both ends are plotted. The solid curve passes through plotted point.
Image with alt text: A coordinate plane's x-axis ranges from negative 1 to 6 and its y-axis ranges from negative 1 to 8, both by 1-unit increments. A solid curve and a dotted line with arrows at both ends are plotted. The solid curve passes through plotted point.
A coordinate plane's axes range from negative 1 to 8, both by 1-unit increments. A solid curve and a dotted line with arrows at both ends are plotted. The solid curve passes through a point plotted on the y-axis.
Image with alt text: A coordinate plane's axes range from negative 1 to 8, both by 1-unit increments. A solid curve and a dotted line with arrows at both ends are plotted. The solid curve passes through a point plotted on the y-axis.
A coordinate plane's axes range from negative 1 to 8, both by 1-unit increments. A solid curve and a dotted line with arrows at both ends are plotted. The solid curve passes through a point plotted on the y-axis.
1. The y-intercept is at (0,6)
.
2. The horizontal asymptote is at y=1
.
3. The graph is decreasing for all values of x.
(1 point)
Responses
A coordinate plane's x-axis ranges from negative 1 to 8 and its y-axis ranges from negative 1 to 8, both by 1-unit increments. A solid curve and a dotted line with arrows at both ends are plotted. The solid curve passes through a plotted point.
Image with alt text: A coordinate plane's x-axis ranges from negative 1 to 8 and its y-axis ranges from negative 1 to 8, both by 1-unit increments. A solid curve and a dotted line with arrows at both ends are plotted. The solid curve passes through a plotted point.
A coordinate plane's x-axis ranges from negative 1 to 6 and its y-axis ranges from negative 1 to 8, both by 1-unit increments. A solid curve and a dotted line with arrows at both ends are plotted. The solid curve passes through plotted point.
Image with alt text: A coordinate plane's x-axis ranges from negative 1 to 6 and its y-axis ranges from negative 1 to 8, both by 1-unit increments. A solid curve and a dotted line with arrows at both ends are plotted. The solid curve passes through plotted point.
A coordinate plane's axes range from negative 1 to 8, both by 1-unit increments. A solid curve and a dotted line with arrows at both ends are plotted. The solid curve passes through a point plotted on the y-axis.
Image with alt text: A coordinate plane's axes range from negative 1 to 8, both by 1-unit increments. A solid curve and a dotted line with arrows at both ends are plotted. The solid curve passes through a point plotted on the y-axis.
A coordinate plane's axes range from negative 1 to 8, both by 1-unit increments. A solid curve and a dotted line with arrows at both ends are plotted. The solid curve passes through a point plotted on the y-axis.
Answers
GPT-4o mini
To determine which graph fits the given properties, we need to analyze each property:
1. The **y-intercept** is at (0,6). This means when \( x = 0 \), the function value (y) must be 6.
2. The **horizontal asymptote** is at \( y = 1 \). This indicates that as \( x \) approaches positive or negative infinity, the function approaches the value of 1.
3. The graph is **decreasing for all values of x**. This means that no matter the value of \( x \), the function overall decreases.
With these properties in mind, you're looking for a graph that starts at (0, 6), continues to decrease, and approaches \( y = 1 \) as \( x \) moves to infinity.
- **Graph 1**: No additional image details provided, but it can be checked against y-intercept and asymptote.
- **Graph 2**: Similar situation as Graph 1, requires checking with the conditions.
- **Graph 3**: Indicates a point on the y-axis; must track if y=6 is satisfied.
Since I cannot see the images, make sure to look for:
- The correct y-intercept at (0,6).
- A graph that approaches the horizontal asymptote of \( y = 1 \) as \( x \) goes to infinity, indicating it should not level off at a value higher than 1.
- Consistently decreasing behavior throughout.
Given your responses, check closely which graph meets all these criteria: y-intercept, horizontal asymptote, and decreasing behavior, and that should lead you to the correct answer!
1. The **y-intercept** is at (0,6). This means when \( x = 0 \), the function value (y) must be 6.
2. The **horizontal asymptote** is at \( y = 1 \). This indicates that as \( x \) approaches positive or negative infinity, the function approaches the value of 1.
3. The graph is **decreasing for all values of x**. This means that no matter the value of \( x \), the function overall decreases.
With these properties in mind, you're looking for a graph that starts at (0, 6), continues to decrease, and approaches \( y = 1 \) as \( x \) moves to infinity.
- **Graph 1**: No additional image details provided, but it can be checked against y-intercept and asymptote.
- **Graph 2**: Similar situation as Graph 1, requires checking with the conditions.
- **Graph 3**: Indicates a point on the y-axis; must track if y=6 is satisfied.
Since I cannot see the images, make sure to look for:
- The correct y-intercept at (0,6).
- A graph that approaches the horizontal asymptote of \( y = 1 \) as \( x \) goes to infinity, indicating it should not level off at a value higher than 1.
- Consistently decreasing behavior throughout.
Given your responses, check closely which graph meets all these criteria: y-intercept, horizontal asymptote, and decreasing behavior, and that should lead you to the correct answer!