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 a Square o Quadratic Function.

b) Independent variable : t , dependent variable : f(t)/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 given by letter that is out of the parentheses. For this exercise,  the name of the function is "f", and it's a Square or Quadratic Function.

The independent variable of a function is the variable we assign the different values. For this exercise, the independent variable is designated with the letter "t".

The dependent variable is the function itself (f(t)), it's also called "y",  and it's called "dependent" variable because its values will always depend on the "independent variable".

A function is the 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 given 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(t), therefore:

f(2)=3*2^{2}-3*2+1=7

Have a nice day!

find the magnitude of the trig term  

csc

(

x

)

−

1

by taking the absolute value of the coefficient.

1

find the lower bound of the range.

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y

=

−

2

find the upper bound of the range.

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y

=

0

the range is  

y

≤

−

2

or  

y

≥

0

.

(

−

∞

,

−

2

]

∪

[

0

,

∞

)

{

y

|

y

≤

−

2

,

y

≥

0

}

step-by-step explanation:

example 2 – simplify: step 1: completely factor both the numerators and denominators of all fractions. step 2: change the division sign to a multiplication sign and flip (or reciprocate) the fraction after the division sign; essential you need to multiply by the reciprocal. step 3 : cancel or reduce the fractions.