f(x) = 10 x^2-9 find domain and range

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f(x) = 10 x^2-9 find domain and range

Mathematics
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are there any values for x that won't work?
9?
sorry i have no idea on where to start

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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
For x^2, any real value will work, right
right
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
so its infinity?
-infinity to +infinity
\(\Large (-\infty,+\infty)\)
THe domain of f is all values for x, such that, x is an element of the reals
so the range would also be (infinity,-infinity)
hmm, look at the function. x^2 is the only variable, x^2 will always be posistive or zero
he's referring to the domain ony thus far =) \(\large \{x|\quad x\in \mathbb{R}\}\)
how does that affect what values f(x) can take
so x would be 9?
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
If x^2 is 0 or larger, how does that limit the values for f(x) ?
something squared will be positive, (-1)^2 = -1 * -1 = +1
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
right I got the graph
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
so in interval notation would it look like (-9,infinity)
bra-ket for the -9, it can be that value
greater than or equal to -9
[-9 , inf)
oh my gosh, okay thank you, im starting to get it now
welcome, takes practicing

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