Question

Which of the following expressions represents a function?

Answer 1

Concept:

A function f from a set A to a set Y is a rule that assigns a unique element f(x) ∈ Y to each element x ∈A.

Points to remember:

1) There is no repetition in the domain of function.

2) Yo can use a 'vertical line test: A function f can have only one value f(x) for each x in its domain, so no vertical line can intersect the graph of a function more than once' to check that whether the given relation is a function.

Now, apply the above two points.

a) x²+y² = 9 , This is the equation of a circle so vertical line intersects the graph at two points, Given relation is not a function.

b) {(4, 2), (4, –2), (9, 3), (9, –3)}, repetition in Domain(4 occurs two times in domain and then 9 occurs two times) so Given relation is not a function.

c) x = 4 , this is a vertical line so repetition in Domain occurs (x=4 infinite values of y occcur) so Given relation is not a function.

d) 2x + y = 5 , equation of a line so according to vertical line test there is no repetition in domain so Given relation is a function.

Answer 2

Definition of a function: a relation that assigns to every x in the domain a unique y value in the range. So, for every input (x value) there can only be one output (y value). That being said we know b cannot be correct because 4 and 9 both have two outputs each. We know it can't be c because the line x=4 is a vertical line at (4,0) which would cause 4 to have infinite outputs. B is definitely a function, because if you divide by 2x you get y=5/2x. If you plug in any value for x it will be a function