## sara1234 3 years ago Find the range of the function. f(x) = (x – 2)^2 + 2 (2 points) All real numbers y ≥ 0 y > 2 y ≥ 2

1. UnkleRhaukus

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

2. helpingtutors

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

3. sami-21

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 ?

4. sara1234

y ≥ 2

5. sara1234

??

6. helpingtutors

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

7. sami-21

yes

8. helpingtutors

think again!!

9. sara1234

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

10. helpingtutors

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?

11. sara1234

all real numbers

12. helpingtutors

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

13. helpingtutors

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

14. helpingtutors

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

15. sara1234

so the answer is all real numbers?

16. sami-21

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 .

17. sara1234

18. helpingtutors

Yes.. y>=2 is right

19. UnkleRhaukus

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