A.give an example of a function whose domain is {3,4,7,9}?

and whose range is {-1,0,3}
B.Find two different functions whose domain is {3,8}and whose range is {-4,1}
C Explain why there does not exist a function whose domain is {-1,0,3} and whose range is [3,4,7,9}
D.Give an example of two different functions f and g ,both of which have the set of real numbers as their domain ,such that f(x)=g(x)for every rational number x
E.Give an exampleof a function whose domain equals the set of real numbers and whose range equals the set of integers
please give me th e detailed explanation
show me the work

A: y = 4 - |x-8|

B:
y = x-7
y = 7 - |x-14|

C: one of the domain values must map to 2 range values. Not a function.

D: tricky, if you want f=g only for rational numbers. If f and g are continuous, then f=g for all reals.

E: y = ⌊x⌋ where ⌊x⌋ is the greatest integer less than or equal to x. Equivalent to x-mod(x,1)

How do you fiind the averege rate change

A. One example of a function whose domain is {3, 4, 7, 9} and whose range is {-1, 0, 3} is:

f(3) = -1
f(4) = 0
f(7) = 3
f(9) = 0

Here, the function assigns each element from the domain to a corresponding element in the range.

B. Two different examples of functions whose domain is {3, 8} and whose range is {-4, 1} are:

Example 1:
f(3) = -4
f(8) = 1

Example 2:
g(3) = 1
g(8) = -4

C. There does not exist a function whose domain is {-1, 0, 3} and whose range is [3, 4, 7, 9] because the range contains more elements than the domain. The number of elements in the domain should be equal to or greater than the number of elements in the range for a function to exist.

D. Two different examples of functions f(x) and g(x) with the domain of the real numbers (R) such that f(x) = g(x) for every rational number x are:

Example 1:
f(x) = x^2
g(x) = x^2

In this case, both functions square the input value, and since squaring preserves the equality of rational numbers, f(x) = g(x) for every rational number x.

Example 2:
f(x) = sin(x)
g(x) = sin(x)

Here, both functions compute the sine of the input value, which is the same for the same rational input values.

E. An example of a function whose domain is the set of real numbers and whose range is the set of integers is:

f(x) = floor(x)

In this case, the function takes any real number x and rounds it down to the nearest integer, producing an integer as the output. The range of this function is the set of all integers.

A. To find a function with a specific domain and range, you can simply assign values from the domain to the corresponding values in the range. For example, let's say we want a function whose domain is {3, 4, 7, 9} and whose range is {-1, 0, 3}.

One possible example of such a function would be:
f(3) = -1
f(4) = 0
f(7) = 3
f(9) = -1

Note that there can be multiple valid functions with the same domain and range.

B. Similarly, to find two different functions with a given domain and range, you can assign different values from the domain to the corresponding values in the range. For example, let's say we want two different functions with a domain of {3, 8} and a range of {-4, 1}.

One possible example of such functions would be:
f(3) = -4 and g(3) = -4
f(8) = 1 and g(8) = -4

C. There does not exist a function whose domain is {-1, 0, 3} and whose range is [3, 4, 7, 9] because functions must have unique outputs for each input. In this case, the range has four distinct values (3, 4, 7, 9), but the domain only has three elements. Since a function cannot map multiple inputs to the same output, it is not possible to find a suitable function in this case.

D. To find two different functions f and g such that f(x) = g(x) for every rational number x, you can choose any two functions that have the same output for every rational number. For example:

f(x) = x^2
g(x) = x^2 + 1

Both of these functions are defined for all real numbers, and for any rational number input, they will yield the same output:
f(x) = g(x) = x^2 for every rational number x.

E. An example of a function with a domain equal to the set of real numbers and a range equal to the set of integers is a step function. A step function divides the real number line into intervals and assigns integer values to each interval.

For example, consider the step function f(x) defined as:
f(x) = floor(x)

Here, the domain is the set of real numbers (since the floor function can be applied to any real number), and the range is the set of integers (as the floor function outputs integers).