Question
which statements about the domain and range of the part of the function shown?
select TWO correct answers.
a the domain is the set of all real numbers greater than 1 and less than or equal to 5
b the range is the set of all real numbers greater than 1 and less than or equal to 5
c the domain is the set of all real numbers greater than or equal to 0 and less than 4
d the domain is the set of all real numbers
select TWO correct answers.
a the domain is the set of all real numbers greater than 1 and less than or equal to 5
b the range is the set of all real numbers greater than 1 and less than or equal to 5
c the domain is the set of all real numbers greater than or equal to 0 and less than 4
d the domain is the set of all real numbers
Answers
GPT-4o mini
To evaluate the correct statements about the domain and range of the function, we need to focus on the definitions of domain and range.
- **Domain** refers to the set of all possible input values (typically \(x\) values) for the function.
- **Range** refers to the set of all possible output values (typically \(y\) values) that a function can produce.
Since the specific function and its graph are not provided, I can guide you through the logic based on the given options.
Based on the provided statements, you can determine two correct answers as follows:
- If the part of the function shown restricts \(x\) values to between certain points (like between 1 and 5 or between 0 and 4), then those constraints will define the domain.
- Similarly, the outputs (y-values) of the function will determine the range.
Let’s analyze the options:
- **Option A**: "the domain is the set of all real numbers greater than 1 and less than or equal to 5."
- This implies a specific segment of the x-axis for the function inputs. If this aligns with the shown function, this could be correct.
- **Option B**: "the range is the set of all real numbers greater than 1 and less than or equal to 5."
- If the outputs of the function fall within this range, this could be correct.
- **Option C**: "the domain is the set of all real numbers greater than or equal to 0 and less than 4."
- This too may be a correct domain if the function only exists within those x-values.
- **Option D**: "the domain is the set of all real numbers."
- This statement could only be true if the function is defined for every real number without any restriction, which is typically less common for specific functions shown on a graph.
To select the TWO correct answers, verify which option seems more aligned with the function presented. If the function strictly shows values in a certain range or is limited to specific inputs, options A and/or C could be correct for the domain, while B may be correct for the range if the output corresponds.
Without additional context from the graph of the function, the correct selections cannot be definitively stated. If you see a limited input range (like between 1 and 5 or 0 and 4), you'd choose accordingly. If both the domain and range can be perfectly defined by options A and B or A and C, select those accordingly.
- **Domain** refers to the set of all possible input values (typically \(x\) values) for the function.
- **Range** refers to the set of all possible output values (typically \(y\) values) that a function can produce.
Since the specific function and its graph are not provided, I can guide you through the logic based on the given options.
Based on the provided statements, you can determine two correct answers as follows:
- If the part of the function shown restricts \(x\) values to between certain points (like between 1 and 5 or between 0 and 4), then those constraints will define the domain.
- Similarly, the outputs (y-values) of the function will determine the range.
Let’s analyze the options:
- **Option A**: "the domain is the set of all real numbers greater than 1 and less than or equal to 5."
- This implies a specific segment of the x-axis for the function inputs. If this aligns with the shown function, this could be correct.
- **Option B**: "the range is the set of all real numbers greater than 1 and less than or equal to 5."
- If the outputs of the function fall within this range, this could be correct.
- **Option C**: "the domain is the set of all real numbers greater than or equal to 0 and less than 4."
- This too may be a correct domain if the function only exists within those x-values.
- **Option D**: "the domain is the set of all real numbers."
- This statement could only be true if the function is defined for every real number without any restriction, which is typically less common for specific functions shown on a graph.
To select the TWO correct answers, verify which option seems more aligned with the function presented. If the function strictly shows values in a certain range or is limited to specific inputs, options A and/or C could be correct for the domain, while B may be correct for the range if the output corresponds.
Without additional context from the graph of the function, the correct selections cannot be definitively stated. If you see a limited input range (like between 1 and 5 or 0 and 4), you'd choose accordingly. If both the domain and range can be perfectly defined by options A and B or A and C, select those accordingly.