Question

Which of the following is not a function?

A. y=5
B. {(1,2), (2,3), (3,4), (4,5)}
C. y=3x+2
D. They are all functions

Answer 1

A function is a relation where each input value corresponds to exactly one output value. Option D, 'They are all functions' is the incorrect choice because it implies that there are no relations that are not functions.

Step-by-step explanation:

To determine which of the given options is not a function, we need to understand what makes a relation a function. A function is a relation where each input value (x) corresponds to exactly one output value (y). If there is at least one input value that corresponds to more than one output value, then the relation is not a function.

Regarding the given options:

1. A. y=5: This is a function because for any input value of x, the output value is always 5. Each input corresponds to exactly one output.
2. B. {(1,2), (2,3), (3,4), (4,5)}: This is a function because each input corresponds to exactly one output. There are no repeated input values.
3. C. y=3x+2: This is a function because each input corresponds to exactly one output. The equation represents a linear function.
4. D. They are all functions: This option is incorrect because, according to the explanation above, if there is at least one input value that corresponds to more than one output value, the relation is not a function. Therefore, option D is not a function.

Therefore, the correct answer is D. They are all functions.