Question

can some one help me with this iv been stuck for about a week and i need some help are these function why or why not? thanks!

Answer 1

Answer:

1) f(x) is not a function

2) g(x) is  a function.

Step-by-step explanation:

Function is  defined as a relationship between the independent variable and  the dependent variable

If a variable y is so related to a variable x that whenever a numerical value is assigned to x, there is a rule according to which a unique value of y is determined, then y is said to be a function of the independent variable

The above function can be represented by y = f(x).  f(x) can also been represented g(x) and P(x) functions of the independent variable x,  when the   function is unknown or unspecified.

Two laws to become a function:

a) Every element in X is related to some element in Y.

This relationship is commonly symbolized as y = f(x). In addition to f(x), other abbreviated symbols such as g(x) and P(x) are often used to represent functions of the independent variable x, especially when the nature of the function is unknown or unspecified.

Two rules to become a function:

a)"Each element" means that every element in X is related to some element in Y.

But some elements of Y may not assigned to x

b) A function is assigned to a single value. It will not give back 2 or more elements for the same input.

One-to-many is unaccepted, while many-to-one is accepted

If the relationship does not satisfies those two rules then it is not a function. we can say that the given relationship not a function.

1) Let f(x) be the function

Given x is domain ie, $x=\{-2-3\}$ and y=f(x) ie, $y=\{2,3\}$ is the range of x

By the definition of function,  f(x) does not satisfies the rules  to be a function because f(-2)=2 and f(-2)=3 So it assigns two values.

Therefore  f(x) is not a function

2) Let g(x) be the function

x is domain ie, $x=\{-2-1,0,1\}$ and y=g(x) ie, $y=\{2,2.5,3,3.5\}$ is the range of x

By the definition function,  g(x)  satisfies the rules  to be a function because g(-2)=3 , g(-1)=3.5,g(0)=2 and g(1)=2 So it assigns exactly one value.

Therefore  g(x) is  a function.