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 function is f.

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

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

d)

Usually, the name of a function is what is out of the parentheses, so the name of the function is "f".

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, 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:

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step-by-step explanation:

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for