Question
A graph where the horizontal axis shows time (t), numbered 1 to 4, and the vertical axis shows height (h) numbered 10 to 60. Solid circles appear at point (0, 48), point (1, 64), point (3, 0). A solid curved line connects all 3 points.
Leon throws a ball off a cliff. The graph represents a relation that models the ball’s height, h, in feet over time, t, in seconds.
What is the domain?
{t| 0 ≤ t ≤ 3}
{t| 0 ≤ t ≤ 48}
{t| 0 ≤ t ≤ 64}
{t| all real numbers}
Leon throws a ball off a cliff. The graph represents a relation that models the ball’s height, h, in feet over time, t, in seconds.
What is the domain?
{t| 0 ≤ t ≤ 3}
{t| 0 ≤ t ≤ 48}
{t| 0 ≤ t ≤ 64}
{t| all real numbers}
Answers
GPT-4o mini
The domain of the graph represents the allowable values of time \( t \) for the height of the ball. From the points you provided, the solid circles are at \( t = 0 \), \( t = 1 \), and \( t = 3 \). There are no points or connections beyond \( t = 3 \), indicating that the ball's height is only modeled between the time of 0 seconds and 3 seconds.
Therefore, the correct domain is:
\[
\{t | 0 \leq t \leq 3\}
\]
Therefore, the correct domain is:
\[
\{t | 0 \leq t \leq 3\}
\]
The mapping diagram shows a relation.
A mapping diagram shows a relation, using arrows, between inputs and outputs for the following ordered pairs: (negative 6, 0), (2, 1), (negative 7, negative 4), (11, 2), (3, 2).
What is the domain of the relation?
{x| x = –4 , 0, 1, 2}.
{x| x = –7, –6, 2, 3, 11}.
{y| y = –4, 0, 1, 2}.
{y| y = –7, –6, 2, 3, 11}.
A mapping diagram shows a relation, using arrows, between inputs and outputs for the following ordered pairs: (negative 6, 0), (2, 1), (negative 7, negative 4), (11, 2), (3, 2).
What is the domain of the relation?
{x| x = –4 , 0, 1, 2}.
{x| x = –7, –6, 2, 3, 11}.
{y| y = –4, 0, 1, 2}.
{y| y = –7, –6, 2, 3, 11}.
GPT-4o mini
The domain of a relation consists of all the unique input values (the first components of the ordered pairs).
From the given ordered pairs:
- (negative 6, 0) → input: -6
- (2, 1) → input: 2
- (negative 7, negative 4) → input: -7
- (11, 2) → input: 11
- (3, 2) → input: 3
Now, collecting all the unique input values, we have:
- -6
- 2
- -7
- 11
- 3
Thus, the domain of the relation is:
\[
\{x | x = -7, -6, 2, 3, 11\}
\]
From the given ordered pairs:
- (negative 6, 0) → input: -6
- (2, 1) → input: 2
- (negative 7, negative 4) → input: -7
- (11, 2) → input: 11
- (3, 2) → input: 3
Now, collecting all the unique input values, we have:
- -6
- 2
- -7
- 11
- 3
Thus, the domain of the relation is:
\[
\{x | x = -7, -6, 2, 3, 11\}
\]
Teresa stated that the heights of the students in her class were not a function of their ages. Which reasoning could justify Teresa’s statement?
Two students are the same age but have different heights.
Two students have the same height but different ages.
No two students are the same age or height.
Two students are the same age but have different heights.
Two students have the same height but different ages.
No two students are the same age or height.
GPT-4o mini
Teresa's statement that the heights of the students in her class were not a function of their ages can be justified by the reasoning:
**Two students are the same age but have different heights.**
In mathematical terms, for a relation to be considered a function, each input (age) must be associated with exactly one output (height). If two students are the same age but have different heights, this means that a single input (age) leads to multiple outputs (heights), which violates the definition of a function.
**Two students are the same age but have different heights.**
In mathematical terms, for a relation to be considered a function, each input (age) must be associated with exactly one output (height). If two students are the same age but have different heights, this means that a single input (age) leads to multiple outputs (heights), which violates the definition of a function.
Which represents a function?
A 2-column table with 5 rows. The first column is labeled x with entries negative 10, negative 5, 0, 5, 10. The second column is labeled y with entries 84, 31.5, 4, 1.5, 24.
A mapping diagram shows a relation, using arrows between domain and range for the following ordered pairs: (8, negative 4), (negative 2, 10), (negative 2, negative 7). In the domain, the number 3 does not have a relation to a number in the range.
A series of ordered pairs: (4, 5), (6, negative 2), (negative 5, 0), (6, 1)
A 2-column table with 5 rows. The first column is labeled x with entries negative 10, negative 5, 0, 5, 10. The second column is labeled y with entries 84, 31.5, 4, 1.5, 24.
A mapping diagram shows a relation, using arrows between domain and range for the following ordered pairs: (8, negative 4), (negative 2, 10), (negative 2, negative 7). In the domain, the number 3 does not have a relation to a number in the range.
A series of ordered pairs: (4, 5), (6, negative 2), (negative 5, 0), (6, 1)
GPT-4o mini
To determine which of the given options represents a function, we need to apply the definition of a function: each input (or x-value) must be associated with exactly one output (or y-value).
1. **2-column table**:
- The entries in the first column (x-values) are: -10, -5, 0, 5, 10.
- Each x-value has a corresponding y-value in the second column (y-values): 84, 31.5, 4, 1.5, 24.
- Since each x-value is unique and does not repeat, this represents a function.
2. **Mapping diagram**:
- The ordered pairs given are: (8, -4), (-2, 10), (-2, -7).
- The x-value -2 is associated with two different y-values (10 and -7).
- This violates the definition of a function, as one input corresponds to multiple outputs.
3. **Series of ordered pairs**:
- The pairs are: (4, 5), (6, -2), (-5, 0), (6, 1).
- The x-value 6 appears twice but is associated with two different y-values (-2 and 1).
- This also does not represent a function.
Based on the reasoning above, the only option that represents a function is:
**The 2-column table with the entries: -10, -5, 0, 5, and 10 in the x column corresponding to 84, 31.5, 4, 1.5, and 24 in the y column.**
1. **2-column table**:
- The entries in the first column (x-values) are: -10, -5, 0, 5, 10.
- Each x-value has a corresponding y-value in the second column (y-values): 84, 31.5, 4, 1.5, 24.
- Since each x-value is unique and does not repeat, this represents a function.
2. **Mapping diagram**:
- The ordered pairs given are: (8, -4), (-2, 10), (-2, -7).
- The x-value -2 is associated with two different y-values (10 and -7).
- This violates the definition of a function, as one input corresponds to multiple outputs.
3. **Series of ordered pairs**:
- The pairs are: (4, 5), (6, -2), (-5, 0), (6, 1).
- The x-value 6 appears twice but is associated with two different y-values (-2 and 1).
- This also does not represent a function.
Based on the reasoning above, the only option that represents a function is:
**The 2-column table with the entries: -10, -5, 0, 5, and 10 in the x column corresponding to 84, 31.5, 4, 1.5, and 24 in the y column.**
Which graph does not represent a function?
On a coordinate plane, a curved crosses the y-axis 1 time and the x-axis 2 times.
On a coordinate plane, a straight line with a negative slope crosses the y-axis 1 time and the x-axis 1 time.
On a coordinate plane, an oval line crosses the y-axis 2 times and the x-axis two times.
On a coordinate plane, a line with an s curve crosses the y-axis 1 time and the x-axis 1 time.
On a coordinate plane, a curved crosses the y-axis 1 time and the x-axis 2 times.
On a coordinate plane, a straight line with a negative slope crosses the y-axis 1 time and the x-axis 1 time.
On a coordinate plane, an oval line crosses the y-axis 2 times and the x-axis two times.
On a coordinate plane, a line with an s curve crosses the y-axis 1 time and the x-axis 1 time.
GPT-4o mini
To determine which graph does not represent a function, we can use the **Vertical Line Test**. According to this test, if a vertical line crosses the graph at more than one point, then the graph does not represent a function, because that would mean a single input (x-value) produces multiple outputs (y-values).
Let's analyze each option:
1. **Curved graph that crosses the y-axis 1 time and the x-axis 2 times**: This could potentially be a function, as long as no vertical line crosses it at more than one point.
2. **Straight line with a negative slope that crosses the y-axis 1 time and the x-axis 1 time**: This definitely represents a function because straight lines will never fail the vertical line test.
3. **Oval line that crosses the y-axis 2 times and the x-axis 2 times**: An oval shape often indicates that this graph would fail the vertical line test, as a vertical line could intersect the oval at more than one point. Therefore, this graph likely does not represent a function.
4. **Line with an s curve that crosses the y-axis 1 time and the x-axis 1 time**: Depending on the shape of the 's' curve, it may or may not be a function. If the 's' curve is a smooth curve resembling a sine wave that goes up and down, then it would also likely fail the vertical line test at certain points.
Based on this analysis, the graph that does not represent a function is:
**The oval line that crosses the y-axis 2 times and the x-axis 2 times.**
Let's analyze each option:
1. **Curved graph that crosses the y-axis 1 time and the x-axis 2 times**: This could potentially be a function, as long as no vertical line crosses it at more than one point.
2. **Straight line with a negative slope that crosses the y-axis 1 time and the x-axis 1 time**: This definitely represents a function because straight lines will never fail the vertical line test.
3. **Oval line that crosses the y-axis 2 times and the x-axis 2 times**: An oval shape often indicates that this graph would fail the vertical line test, as a vertical line could intersect the oval at more than one point. Therefore, this graph likely does not represent a function.
4. **Line with an s curve that crosses the y-axis 1 time and the x-axis 1 time**: Depending on the shape of the 's' curve, it may or may not be a function. If the 's' curve is a smooth curve resembling a sine wave that goes up and down, then it would also likely fail the vertical line test at certain points.
Based on this analysis, the graph that does not represent a function is:
**The oval line that crosses the y-axis 2 times and the x-axis 2 times.**
the one that is a circle click that one guys
GPT-4o mini
Thank you for your clarification. A circle indeed does not represent a function because it fails the Vertical Line Test: there are vertical lines that can intersect the circle at two points.
So, based on your mention of "the one that is a circle," the correct answer to your question of which graph does not represent a function is:
**The oval line (circle) that crosses the y-axis 2 times and the x-axis 2 times.**
This graph fails the vertical line test because a vertical line drawn at certain x-values will intersect the circle at two distinct points, indicating that it does not have a unique y-value for each x-value. Thank you for pointing that out!
So, based on your mention of "the one that is a circle," the correct answer to your question of which graph does not represent a function is:
**The oval line (circle) that crosses the y-axis 2 times and the x-axis 2 times.**
This graph fails the vertical line test because a vertical line drawn at certain x-values will intersect the circle at two distinct points, indicating that it does not have a unique y-value for each x-value. Thank you for pointing that out!