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A quadratic function: f(x) = ax2 + bx + c = 0, where a ≠ 0.
Domain: {x| x is a real number}, or in the interval notation, (-∞, ∞).
Range:
If a > 0, {y| y ≥ f(-b/2a), the y-coordinate of the vertex} or [f(-b/2a), ∞).
If a < 0, {y| y ≤ f(-b/2a), the y-coordinate of the vertex} or (-∞, f(-b/2a)].
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Alternative answer:
The domain is anything you chose it to be. For example, the integers between 2.5 and 4.7 (ie 3 and 4) and the real numbers between 4.8 and 5.0.
Then the range would be the values of f(x) which corresponded to the values of x in the domain.
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When can a quadratic function have an inverse?
It depends on the domain and codomain. In complex numbers, that is, when the domain and codomain are both C, every quadratic always has an inverse.If the range of the quadratic in the form ax2 + bx + c = 0 is the set of real numbers, R, then the function has an inverse if(a) b2 - 4ac ≥ 0and(b) the range of the inverse is defined as x ≥ 0 or x ≤ 0
How do you find the domain if you are given the range?
Use the function to find the image of each point in the domain. The set of values that you get will be the range. If the function is well behaved, you will not have to try each and every value in the domain.
How does the domain relate to a function?
Any function is a mapping from a domain to a codomain or range. Each element of the domain is mapped on to a unique element in the range by the function.
What is the domain and range for the following function and its inverse f of x equals -x plus 5?
The function is a simple linear function and so its nature does not limit the domain or range in any way. So the domain and range can be the whole of the real numbers. If the domain is a proper subset of that then the range must be defined accordingly. Similarly, if the range is known then the appropriate domain needs to be defined.
What is the function of relation domain and range in mathematics?
A relation is a mapping from elements of one set, called the domain, to elements of another set, called the range. The function of the three terms: relation, domain and range, is to define the parameters of a mapping which may or may not be a function.
