Question

Which of the following is/are function?

• A.
• B. $f:X\to YX:\{2,3,4,5\}Y:\{3,4,5,2\}f=\left\{\right(2,3),(3,5),(4,5),(5,4\left)\right\}$
• C.
• D.

Answer 1

Answer: (B), (C), (D)

We know the relation can be function only when each and every input is mapped with exactly one output value or each input is associated with unique output.

Now we check all options
As, Input value $3$ is not mapped with any value of output values so this is not a function.

Now, in option$\left(b\right)$, every element of set $X$ is associated with exactly one element of set $Y$. Hence, it a function.

In tabular form, every input values$\left(X\right)$ gives different output$\left(Y\right)$. So, it is also function.

In last option we will apply vertical line test for the given graph by drawing vertical line to the curve and check if the line is cutting the curve at one point or more.
as there is no such vertical line which cut the curve at more than one point so it is also function.