Question
Give the domain and range of the quadratic function whose graph is described.
Minimumequalsnegative 6 at xequals3
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Part 1
The domain of the function is
enter your response here. (Type your answer in interval notation.)
Minimumequalsnegative 6 at xequals3
Question content area bottom
Part 1
The domain of the function is
enter your response here. (Type your answer in interval notation.)
Answers
GPT-4o mini
For a quadratic function, the domain is always all real numbers, unless stated otherwise.
So, the domain of the function is:
\[
(-\infty, +\infty)
\]
Now, regarding the range, since the graph has a minimum value of -6 at \(x = 3\), and it opens upwards (as it has a minimum), the range starts from this minimum value and goes to positive infinity.
Thus, the range of the function is:
\[
[-6, +\infty)
\]
In summary:
- **Domain**: \((- \infty, + \infty)\)
- **Range**: \([-6, +\infty)\)
So, the domain of the function is:
\[
(-\infty, +\infty)
\]
Now, regarding the range, since the graph has a minimum value of -6 at \(x = 3\), and it opens upwards (as it has a minimum), the range starts from this minimum value and goes to positive infinity.
Thus, the range of the function is:
\[
[-6, +\infty)
\]
In summary:
- **Domain**: \((- \infty, + \infty)\)
- **Range**: \([-6, +\infty)\)