Answer :
Answer:
- Domain = [-3, 2)
- Range = [-4, 5]
Explanation
The domain is the set of all possible input values of x.
The graph your teacher gave you shows that x = -3 is the smallest input allowed, i.e. left-most, while x = 2 is the farthest we can go to the right. However, due to the open hole, x = 2 isn't actually part of the domain.
The domain as an inequality is -3 ≤ x < 2 which will condense to the interval notation [-3, 2)
Two things to notice:
- The square bracket is used to include the -3 since we have a filled in endpoint here.
- The curved parenthesis is used to exclude the endpoint 2 because of the open hole. Think of it like a pothole you cannot drive over. We can get closer and closer to x = 2, but not reach the actual value itself.
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The range is the set of possible y outputs.
The graph indicates we can go as low as y = -4 and as high as y = 5.
The range as an inequality is therefore -4 ≤ y ≤ 5 which condenses to the interval notation [-4, 5]
This time both endpoints are included since the open hole is not located at the very top nor very bottom of the curve.
Answer: Domain: [-3, 2)
Range: [-4, 5]
Step-by-step explanation: The domain refers to the entire set of x-values that the graph contains. When writing the domain or range, you use either brackets or parentheses, followed by two numbers separated by commas that indicate the set of values the graph contains.
Brackets indicate that the number adjacent to it is included within the domain/range, while parentheses indicate that the number adjacent to it is not included. Since there is a closed circle at x=-3, that means that -3 is included in the domain. Since there is an open circle at x=2, that indicates that x=2 is not included within the domain.
The range represents the entire set of y-values that the graph contains. Since there is a continuous line ranging from y = -4 to y=5, the entire set of numbers between these values is included in the range.
