what is the domain and range of this question and how would you work it out y=f(x)=-x^2+3.?

Question

the domain and range is suppose to be in interval notation

Answer 1

The domain of a function is the set of possible inputs for the function. If the function is given without its doman, you assume that the domain is the largest possible set of numbers for which the function gives sensible outputs. Of course, context is important - you could state that the domain of this function is the set of all complex numbers, or an even larger set (the quaternions perhaps?), since it gives sensible outputs for all of them, but since your teacher wants the answer in interval notation, she obviously wants you to consider only real inputs, so the domain is all real numbers or (-∞, ∞).

The range of a function is the set of possible outputs that the function can give when fed an input in its domain. Here, note that x² will always be nonnegative assuming real inputs, so -x² ≤ 0. Therefore, -x²+3 ≤ 3, so the range of the function is all real numbers less than or equal to three, which in interval notation is (-∞, 3].

Answer 2

The domain -- the set of all numbers that we're allowed to use for x -- will be ( -infinity, +infinity ). That's because there are no values of x that would break any mathematical laws, like dividing by zero, nor any values that we're specifically forbidden from using.

The range, on the other hand, the set of all values that the function can produce, is *not* infinite in both directions. If you were to sketch a graph of this curve, it would look like a parabola, opening downwards (like a frown, instead of a smile, if that helps you picture it), reaching its highest point when x = 0. And when x = 0, f(0) = -0² + 3 = 0 + 3 = 3. This point (0,3) is called the parabola's "vertex," and since the parabola opens downwards, the vertex will be its highest point. So y can become infinitely negative, but can't go any higher than 3. That means the range is ( -infinity, 3 ] .

See the link below for more info. Hope that helps!

Answer 3

y = f(x) = -x^2 + 3

Domain: All numbers "x" can be. Are there any numbers that DON'T work for "x"? Can you square any number?
Yes. So, domain is (-infinity,infinity)

Range: All numbers "y" can be. Solve for "x" in terms of "y" first:
y = - x^2 + 3
3 - y = x^2
x = sqrt(3 - y)
Are there any numbers "y" cannot be? Analyze the equation. You know you cannot have a negative number under the "sqrt"

So, 3 - y >= 0
y <=3
Range: (-infinity,3 ] You need the bracket instead of the parenthesis because the range INCLUDES "3"

Answer 4

Domain: (-infinity, +infinity)
Range: [3, + infinity)

Answer 5

domain- ( infinity, Infinity)

range- ( infinity, Infinity)

if you combine like terms it should be -x^5

and since if you plug in any value you can get a value

Answer 6

the function is a parabola
y is min when x=0 i.e 3
y is max when x=infinti,-infiniti i.e infiniti

domain (-infinity,infinity)
range (3,infinity)

Answer 7

domain will be all real numbers.
range will be {3, infinte}