# Sketch the following functions/relations and supply the domain and range. (Label properly) y = {x^2 x<=0 {√x x>0 If it is a function, state whether it is into,...

Sketch the following functions/relations and supply the domain and range. (Label properly)

y = {x^2 x<=0

{√x x>0

If it is a function, state whether it is into, onto or one to one and justify.

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### 1 Answer

A) From the defintion of the relation, we know that the **domain** is `(-oo,oo)`

B) From the following graph we can see that the **range** is `[0,oo)`

This can also be seen that noticing that x^2 is always non-negative and sqrt(x) is also non-negative

C) This relation is a function, and it is **onto **and **into** on the above defined domain and range.

D) It is **not one to one** because

Given x=1, then f(1)=sqrt(1)=1.

In the same time f(-1)=(-1)^2=1

Hence f(1)=f(-1) but 1 not equal (-1)

Please note that even if the graph show a gap, there is none. This a continuous function with value 0 at 0.