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,...

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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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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.

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