Find the range of the function.

f(x) = (x – 2)^2 + 2 (2 points)

All real numbers
y ≥ 0
y 2
y ≥ 2

Question

Find the range of the function.

f(x) = (x – 2)^2 + 2  (2 points)

    All real numbers
    y ≥ 0
    y > 2
    y ≥ 2

unklerhaukus · Answer

its a parabola , ( you can tell because one fo the variables is squared,

a parabola will have either a minimum or maximum value

anonymous · Answer

range of parabola is the range of valid y values!!

anonymous · Answer

put x=2  in the given equation you will be left with only y=2 means regardless values of x it will be y=2
now since it is Parabola which opens upward . so can you tell me what will be the range ?

anonymous · Answer

y ≥ 2

anonymous · Answer

??

anonymous · Answer

Did you find any value of x for which f(x) is undefined?

anonymous · Answer

yes

anonymous · Answer

think again!!

anonymous · Answer

no its not right huh? @sami-21 said yes

anonymous · Answer

yep!!  none of the real value of x make f(x) undefined!!  So all real values of x make f(x) valid!! Therefore, what do you say about the range of y?

anonymous · Answer

all real numbers

anonymous · Answer

Yes..   so, since the term containing x is squared. 
f(x) retains a minimum of 2

anonymous · Answer

hence, y has a restriction  on real numbers as well!!

anonymous · Answer

so what is that you say now on range of y??

anonymous · Answer

so the answer is all real numbers?

anonymous · Answer

when you put x=2 you are left with y=2 this means
whatever the value of x  vale of y (range) will never be less than 2 .

anonymous · Answer

guyss which is the answer!!!!!!!!!!!!!!

anonymous · Answer

Yes.. y>=2 is right

unklerhaukus · Answer

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