Question 2: Which of the following relations are functions?
To determine if a relation is a function, each input (the first element of the ordered pairs) must correspond to exactly one output (the second element of the ordered pairs).
A) (-1, 3), (-4, 3), (-2, 3), (0, 3)
- Inputs: -1, -4, -2, 0
- Each input corresponds to a unique output (3).
- This is a function.
B) (8, 2), (6, -5), (7, -1), (6, 5)
- Inputs: 8, 6, 7, 6
- The input 6 corresponds to two outputs (-5 and 5).
- This is not a function.
C) (2, 4), (2, 7), (2, -1), (2, 0)
- Inputs: 2, 2, 2, 2
- The input 2 corresponds to multiple outputs (4, 7, -1, 0).
- This is not a function.
D) (8, 2), (6, 5), (7, -1), (6, 5)
- Inputs: 8, 6, 7, 6
- The input 6 corresponds to one unique output (5), but the input 6 appears twice with the same output.
- This is a function.
Summary for Question 2:
A is a function, B is not a function, C is not a function, D is a function.
Question 3: Read the given scenarios. Determine if it is a function or not a function.
A function must have a unique output for each input.
A) Input is Student ID number. Output is student age.
- Each student ID corresponds to one unique student age.
- This is a function.
B) The teacher surveys the class. The input is the ages of students in class. The output is the grade level of students in class.
- Different students of the same age may be in different grade levels.
- This is not a function.
C) Input is the year a group of students graduates from high school. Output is a list of their current salaries.
- Multiple groups graduating in the same year can have different salaries.
- This is not a function.
D) Input is your birthday. Output is number of TVs in your house.
- A person's birthday does not uniquely determine the number of TVs in their house.
- This is not a function.
Summary for Question 3:
A is a function, B is not a function, C is not a function, D is not a function.
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