Question
Find the domain and range of the following function.
points on graph are (0,-3) (1.2,0)
Domain: Response area
Range: Response area
answers are: (-∞,∞) , (-4,∞) , (∞,-4) , (-10,3) , [-4,∞)
points on graph are (0,-3) (1.2,0)
Domain: Response area
Range: Response area
answers are: (-∞,∞) , (-4,∞) , (∞,-4) , (-10,3) , [-4,∞)
Answers
GPT-4o mini
To determine the domain and range of the function represented by the points \((0, -3)\) and \((1.2, 0)\), we analyze the information given.
**Domain:**
The domain consists of all the x-values for which the function is defined. From the given points, we have x-values of 0 and 1.2. Therefore, the domain extends from 0 to 1.2. However, since we are looking for the overall range of x-values that includes all possible inputs, we can consider that the function could potentially be defined for all real numbers if it's not constrained, but based on the given points, we can say:
**Domain**: \((-\infty, \infty)\)
**Range:**
The range consists of all the y-values that the function can output. From the points provided:
- At \(x = 0\), \(y = -3\).
- At \(x = 1.2\), \(y = 0\).
Given that these are the only points given and tends to start at \(-3\) (the lowest point) and goes up to \(0\) as x increases, we can infer that the function's outputs (y-values) start from \(-3\) and grow upwards.
Thus, the range based on given points generally can be considered as:
**Range**: \([-3, 0)\)
However, since the specific options you provided do not exactly match our derived range but include \([-4, \infty)\), it can also mean that the function also has potential outputs reaching beyond these limits or similar extensions.
Based on your options for range, we can choose the best possible answer which is:
**Range**: \([-4, \infty)\)
Thus, the final answer is:
- **Domain**: \((-\infty, \infty)\)
- **Range**: \([-4, \infty)\)
**Domain:**
The domain consists of all the x-values for which the function is defined. From the given points, we have x-values of 0 and 1.2. Therefore, the domain extends from 0 to 1.2. However, since we are looking for the overall range of x-values that includes all possible inputs, we can consider that the function could potentially be defined for all real numbers if it's not constrained, but based on the given points, we can say:
**Domain**: \((-\infty, \infty)\)
**Range:**
The range consists of all the y-values that the function can output. From the points provided:
- At \(x = 0\), \(y = -3\).
- At \(x = 1.2\), \(y = 0\).
Given that these are the only points given and tends to start at \(-3\) (the lowest point) and goes up to \(0\) as x increases, we can infer that the function's outputs (y-values) start from \(-3\) and grow upwards.
Thus, the range based on given points generally can be considered as:
**Range**: \([-3, 0)\)
However, since the specific options you provided do not exactly match our derived range but include \([-4, \infty)\), it can also mean that the function also has potential outputs reaching beyond these limits or similar extensions.
Based on your options for range, we can choose the best possible answer which is:
**Range**: \([-4, \infty)\)
Thus, the final answer is:
- **Domain**: \((-\infty, \infty)\)
- **Range**: \([-4, \infty)\)