Please check urgently .I have to submit the assignment

A give an example of a function whose domain equals the set of real numbers and whose range equals the set?
the set {-1,0,1}
BGive an example of a function whose domain equals (0,1)and whose range equals [0,1]
C.Give n example of a function whose is the set of positive integers and whose range is the set of positive even integers
D. Give an example of a function whose domain is the set of positive even integers and whoce range is the set of positive odd integers
Egive an example of function whose domain is the set of integers and whoce range is the set of positive integers.
F. Give an example of function whose domain is the set of positive integers and whoce range is the set of integers.
plese show me the work

Certainly! Let's break down each part and find the answers step by step:

A. Give an example of a function whose domain equals the set of real numbers and whose range equals the set {-1, 0, 1}.

To create such a function, we can consider a function that maps each real number to its sign. Here's an example:

Function: f(x) = x / |x|

Explanation: The function f(x) takes any real number x and divides it by its absolute value (|x|). The result of this division will always be either -1, 0, or 1, matching the range given in the question.

B. Give an example of a function whose domain equals (0, 1) and whose range equals [0, 1].

To create such a function, we can consider a simple identity function that maps each number in the domain to itself. Here's an example:

Function: g(x) = x

Explanation: The function g(x) takes any number x in the open interval (0, 1) and simply returns that same number. Since the range is specified as [0, 1], where both endpoints are included, this function satisfies the given conditions.

C. Give an example of a function whose domain is the set of positive integers and whose range is the set of positive even integers.

To create such a function, we can define a function that doubles the input value. Here's an example:

Function: h(x) = 2x

Explanation: The function h(x) takes any positive integer x and multiplies it by 2. Since multiplying any positive integer by 2 always gives a positive even integer, this function satisfies the given conditions.

D. Give an example of a function whose domain is the set of positive even integers and whose range is the set of positive odd integers.

To create such a function, we can define a function that adds 1 to the input value. Here's an example:

Function: k(x) = x + 1

Explanation: The function k(x) takes any positive even integer x and adds 1 to it. Adding 1 to any positive even integer always results in a positive odd integer, satisfying the given conditions.

E. Give an example of a function whose domain is the set of integers and whose range is the set of positive integers.

To create such a function, we can define a function that takes the absolute value of the input value and adds 1. Here's an example:

Function: l(x) = |x| + 1

Explanation: The function l(x) takes any integer x, computes its absolute value, and then adds 1. This guarantees that the result is always a positive integer, satisfying the given conditions.

F. Give an example of a function whose domain is the set of positive integers and whose range is the set of integers.

To create such a function, we can define a function that multiplies the input value by -1 for odd numbers and leaves it unchanged for even numbers. Here's an example:

Function: m(x) = (-1)^x * ⌊(x+1)/2⌋

Explanation: The function m(x) takes any positive integer x. If x is even, it leaves the value unchanged. If x is odd, it multiplies the value by -1. This function maps positive integers to the set of integers, satisfying the given conditions.

I hope this helps! Remember, you can always verify the answers independently by plugging in values and checking the outputs.