Question 1:
To determine if the relation shown in the table is a function, we need to check if each input \( x \) corresponds to exactly one output \( f(x) \).
Given the data:
- \( f(3) = 2 \)
- \( f(0) = 1 \)
- \( f(5) = -7 \)
- \( f(-3) = 2 \)
In this case, the input \( -3 \) produces the same output \( f(-3) = 2 \) as the input \( 3 \) does. Since there are different inputs (3 and -3) that yield the same output (2), we can conclude:
Response: No, there are multiple outputs with the same input.
Question 2:
Let's analyze each relation to see if they qualify as functions:
-
(8, 2), (6, 5), (7, -1), (6, 5):
- Input \( 6 \) corresponds to two outputs \( 5 \) and \( 5 \) (same). This is a function.
-
(2, 4), (2, 7), (2, -1), (2, 0):
- Input \( 2 \) corresponds to multiple outputs \( 4, 7, -1, 0 \). This is not a function.
-
(-1, 3), (-4, 3), (-2, 3), (0, 3):
- All different inputs correspond to the same output \( 3 \). This is a function.
-
(8, 2), (6, -5), (7, -1), (6, 5):
- Input \( 6 \) corresponds to two different outputs \( -5 \) and \( 5 \). This is not a function.
Responses that are functions:
- (8, 2), (6, 5), (7, -1), (6, 5)
- (-1, 3), (-4, 3), (-2, 3), (0, 3)
Question 3:
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Input is Student ID number. Output is student age.
- This is a function since each student ID corresponds to one unique age.
-
The teacher surveys the class. The input is the ages of students in class. The output is the grade level of students in class.
- This is not a function, as multiple students of the same age may be in different grade levels.
-
Input is the year a group of students graduates from high school. Output is a list of their current salaries.
- This can be considered a function if each year corresponds to a specific group with defined salaries.
-
Input is your birthday. Output is the number of TVs in your house.
- This is not a function since different people with the same birthday may have different numbers of TVs.
Final Assessment:
- Function: Student ID number to student age.
- Not a Function: Ages of students to their grade levels, and birthday to the number of TVs in your house.
- Possibly a Function: Year of high school graduation to current salaries.
If you have any more questions or need further clarification, feel free to ask!