## How do you determine if Y is a function of x?

Vertical line test: If a vertical line can be drawn to touch the graph of a function in more than one place, then �� is NOT a function of ��. If it is not possible to draw a vertical line to touch the graph of a function in more than one place, then y is a function of x.

What is the function of a ring?

Although some people wear rings as mere ornaments or as conspicuous displays of wealth, rings have symbolic functions respecting marriage, exceptional achievement, high status or authority, membership in an organization, and the like.

What is X in ring theory?

Properties that pass from R to R[X] In this section, R is a commutative ring, K is a field, X denotes a single indeterminate, and, as usual, is the ring of integers.

### How do you prove something is a ring?

A ring is a nonempty set R with two binary operations (usually written as addition and multiplication) such that for all a, b, c ∈ R, (1) R is closed under addition: a + b ∈ R. (2) Addition is associative: (a + b) + c = a + (b + c). (3) Addition is commutative: a + b = b + a.

How do you find y in a function?

College Algebra

1. To determine the x-intercept, we set y equal to zero and solve for x. Similarly, to determine the y-intercept, we set x equal to zero and solve for y.
2. To find the x-intercept, set y = 0 \displaystyle y=0 y=0.
3. To find the y-intercept, set x = 0 \displaystyle x=0 x=0.

How do you determine an equation is a function?

Determining whether a relation is a function on a graph is relatively easy by using the vertical line test. If a vertical line crosses the relation on the graph only once in all locations, the relation is a function. However, if a vertical line crosses the relation more than once, the relation is not a function.

#### Is Z is a ring?

The integers Z with the usual addition and multiplication is a commutative ring with identity.

How do you find the perfect ring?

We can make a similar construction in any commutative ring R: start with an arbitrary x ∈ R, and then identify with 0 all elements of the ideal xR = { x r : r ∈ R }. It turns out that the ideal xR is the smallest ideal that contains x, called the ideal generated by x.

What is the identity of a ring?

A ring with identity is a ring R that contains an element 1R such that (14.2) a ⊗ 1R = 1R ⊗ a = a , ∀ a ∈ R . Let us continue with our discussion of examples of rings. Example 1. Z, Q, R, and C are all commutative rings with identity.

## Is Zn a ring?

Zn is a ring, which is an integral domain (and therefore a field, since Zn is finite) if and only if n is prime. For if n = rs then rs = 0 in Zn; if n is prime then every nonzero element in Zn has a multiplicative inverse, by Fermat’s little theorem 1.3. 4.