Question

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.

Answer 1

Hello!

The answers are:

a) The name of the function is f.

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

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

d) $f(-5)=-3t^{2}-2t=-3*(-5)^{2}-2*(-5)=-75+10=-65$

Why?

Usually, the name of a function $f(x)$ 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 "t"

The dependent variable is the function itselft, it's also called "y", it's called "dependent" variable because its values will always depends of the "independent variable"

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 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, so:

$f(-5)=-3t^{2}-2t=-3*(-5)^{2}-2*(-5)=-75+10=-65$

Have a nice day!