## anonymous one year ago f(x) = 10 x^2-9 find domain and range

1. DanJS

are there any values for x that won't work?

2. anonymous

9?

3. anonymous

sorry i have no idea on where to start

4. DanJS

nah, x=9 will return a value for f(x) THe domain is all the input values that work the range is the values f(x) takes

5. DanJS

For x^2, any real value will work, right

6. anonymous

right

7. DanJS

THe parabola opens in the vertical direction, it gets wider and wider forever, the values for x can be any real value That is the domain

8. anonymous

so its infinity?

9. DanJS

-infinity to +infinity

10. jdoe0001

$$\Large (-\infty,+\infty)$$

11. DanJS

THe domain of f is all values for x, such that, x is an element of the reals

12. anonymous

so the range would also be (infinity,-infinity)

13. DanJS

hmm, look at the function. x^2 is the only variable, x^2 will always be posistive or zero

14. jdoe0001

he's referring to the domain ony thus far =) $$\large \{x|\quad x\in \mathbb{R}\}$$

15. DanJS

how does that affect what values f(x) can take

16. anonymous

so x would be 9?

17. DanJS

no x will be any real number, from the domain we just figured f(x) may be limited to some interval(s) sometimes, depending on the nature of the function

18. DanJS

If x^2 is 0 or larger, how does that limit the values for f(x) ?

19. DanJS

something squared will be positive, (-1)^2 = -1 * -1 = +1

20. DanJS

To graph this parabola, you probably will figure the vertex point, and the + on the ax^2 term means it opens toward the +y direction

21. anonymous

right I got the graph

22. DanJS

if x^2 is always 0 or larger, the smallest value for f(x) is when x = 0 , and f(x) = -9, and the thing opens towards positive y. the values for f(x), THE RANGE , is then limited to y values greater than or equal to -9

23. anonymous

so in interval notation would it look like (-9,infinity)

24. DanJS

bra-ket for the -9, it can be that value

25. DanJS

greater than or equal to -9

26. DanJS

[-9 , inf)

27. anonymous

oh my gosh, okay thank you, im starting to get it now

28. DanJS

welcome, takes practicing