Hello!
A cubic function is in the form of
.
All cubic functions have a domain of all real numbers, the range also has a range of all real numbers.
Interval notation is used for representing a function/interval as a pair of numbers. Parentheses and brackets are used to show if the endpoints of a given function/interval are included or excluded. Brackets allow the endpoints to be included while parentheses exclude the endpoint.
Our first instinct would be that the domain is written as [-∞, ∞], but that is incorrect. Infinity is not a number, but it is a concept. This means that they are excluded from the domain.
Therefore, the domain of the function f(x) is (-∞, ∞).
The <em>xy</em>-plane has a normal vector of 〈0, 0, 1〉, and any plane parallel to it will have the same normal vector.
Then the equation of the plane through (6, 3, 2) that is parallel to the <em>xy</em>-plane has equation
〈<em>x</em> - 6, <em>y</em> - 3, <em>z</em> - 2〉 • 〈0, 0, 1〉 = 0
==> <em>z</em> - 2 = 0
==> <em>z</em> = 2