Question

how do you find the range of f(x)=3-x^2 PLEASE HELP

Answer 1

the range of a function is all the values that can be output
the domain, on the other hand, is all values that can be input

for instance:

y = x^2

x can equal... 1, 2,3, 100000000000, -43242342, pi, e, another variable... anything.
it is said that the "domain of x is all real numbers" meaning that the values that can be input into y=x^2 are all real numbers.

so, likewise, once you know the domain you can obtain the range easily. If you know what can be input into an equation, then you must know what can be output from that equation right???

with y = x^2, since the domain is all real numbers, the range is also all real numbers greater than or equal to 0. Why is this? Well, notice whenever you input ANY number into the equation, it's always positive, and always at least equal to zero... thus that's the range.

so, for your equation f(x)=3-x^2... is it any different than y = x^2? it generally helps by having a graph

Answer 2

we're not aloud to use a graph! i dont understand how to know what the output is!

Answer 3

but thank you so much!

Answer 4

you don't necissarily need to draw the graph out, but just know what the graph of

y=x^2

looks like

then that can help you determine what the graph of

y = 3 - x^2

will look like, and if you know the domain/range of y = x^2, which is a very basic function, you can EASILY, easily, easily, find the domain/range of the function you asked : )

Answer 5

but howwww my brain hurts!