For each function, do the following: a) state the name of the function, b) identify the independent and dependent variable, c) identify the rule that assigns exactly one output to the very input, and d) evaluate the function for the given input value.

The answers are:

a) The name of the function is f, and it's an Absolute Value Function.

b) Independent variable : x , dependent variable : f(x)/y

c) The rule that assigns exactly one output to the very input is called "function".

d)

Usually, the name of a function (f(x)) is the letter that is out of the parentheses, so, for this case,  the name of the function is "f", and it's an Absolute Value Function.

The independent variable of a function is the variable we assign the different values, so, for this case, the independent variable is designated with the letter "x".

The dependent variable is the function itself (f(x)), it's also called "y", it's called "dependent" variable because its values will always depend on the "independent variable".

A function is a rule that states that there is exactly one output (range value) to the very input (domain value).  A function only exists when there is exactly one output value (range) for each input (domain), if there is more than one output for each input, the function does not exist.

Evaluating a function consists of assign values to the independent variable(x), hence:

Have a nice day!

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below: