Question
the graph shows an exponential function
both axises range from -10 to 10.
a dot is place at 3, 2. it curves upwards into the top left quadrant. it intersects at the points 1, 3. 0, 4. -1, 5, and it almost intersects at -2, 6 but not quite. it does also intersect at -3, 8, though.
which inequality represents the domain of the part shown?
X is less than or equal to 3
Y is greater than 0
X is less than 0
Y is greater than or equal to 2.
both axises range from -10 to 10.
a dot is place at 3, 2. it curves upwards into the top left quadrant. it intersects at the points 1, 3. 0, 4. -1, 5, and it almost intersects at -2, 6 but not quite. it does also intersect at -3, 8, though.
which inequality represents the domain of the part shown?
X is less than or equal to 3
Y is greater than 0
X is less than 0
Y is greater than or equal to 2.
Answers
Answered by
GPT-4o mini
To determine the appropriate inequalities representing the domain of the part of the exponential function shown in the graph, we can analyze the information provided:
1. The dot is placed at (3, 2), indicating that the curve starts there and continues to rise as it moves left.
2. The curve intersects with the y-axis at several points: (1, 3), (0, 4), (-1, 5), and nearing (-2, 6), but definitely intersects at (-3, 8).
3. The graph appears to be in the upper part of the coordinate plane and curving upwards into the top left quadrant, meaning the y-values are positive.
Based on this information, we can make the following assessments:
- Since the curve starts at x = 3 and extends to the left without bound, the inequality for x would be \( X \leq 3 \).
- Given that the y-values begin at 2 when x equals 3 and go upwards as x decreases, this implies \( Y \geq 2 \).
Thus, we can summarize the inequalities for the domain of the part shown:
- **X is less than or equal to 3** (i.e., \( X \leq 3 \)).
- **Y is greater than or equal to 2** (i.e., \( Y \geq 2 \)).
So the correct inequalities to represent the domain of the part shown are:
\[ X \leq 3 \] and \( Y \geq 2 \).
1. The dot is placed at (3, 2), indicating that the curve starts there and continues to rise as it moves left.
2. The curve intersects with the y-axis at several points: (1, 3), (0, 4), (-1, 5), and nearing (-2, 6), but definitely intersects at (-3, 8).
3. The graph appears to be in the upper part of the coordinate plane and curving upwards into the top left quadrant, meaning the y-values are positive.
Based on this information, we can make the following assessments:
- Since the curve starts at x = 3 and extends to the left without bound, the inequality for x would be \( X \leq 3 \).
- Given that the y-values begin at 2 when x equals 3 and go upwards as x decreases, this implies \( Y \geq 2 \).
Thus, we can summarize the inequalities for the domain of the part shown:
- **X is less than or equal to 3** (i.e., \( X \leq 3 \)).
- **Y is greater than or equal to 2** (i.e., \( Y \geq 2 \)).
So the correct inequalities to represent the domain of the part shown are:
\[ X \leq 3 \] and \( Y \geq 2 \).