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

Question

danjs · Answer

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

anonymous · Answer

9?

anonymous · Answer

sorry i have no idea on where to start

danjs · Answer

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

danjs · Answer

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

anonymous · Answer

right

danjs · Answer

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

anonymous · Answer

so its infinity?

danjs · Answer

-infinity to +infinity

jdoe0001 · Answer

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

danjs · Answer

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

anonymous · Answer

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

danjs · Answer

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

jdoe0001 · Answer

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

danjs · Answer

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

anonymous · Answer

so x would be 9?

danjs · Answer

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

danjs · Answer

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

danjs · Answer

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

danjs · Answer

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

anonymous · Answer

right I got the graph

danjs · Answer

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

anonymous · Answer

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

danjs · Answer

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

danjs · Answer

greater than or equal to -9

danjs · Answer

[-9 , inf)

anonymous · Answer

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

danjs · Answer

welcome, takes practicing