Question

f(x) = -8x – 9; find f(-3)

Answer 1

We will investigate how to evaluate a function given an input value.

A function is defined as a unique relationship between an input and an output variable. Furthermore, for each value of an input there is a unique value of an output. In graphical terms all functions qualify the vertical line test.

A function is expressed in terms of an independent variable also called as an input variable. It is defined over the domain of indepedent variable which expresses a set of values that are of control, whereas, the output of a function depends on its domain.

We are given the following function as follows:

$f\text{ ( x ) = -8x - 9}$

The above function is defined for all real values of ( x ) unless specified in the context of the problem. We can go ahead and write down the domain of the above function as follows:

$\text{\textcolor{#FF7968}{Domain:}}\text{ ( -}\infty\text{ , }\infty\text{ )}$

We are to evaluate the given function [ f ( x ) ] for one of the values from the domain expressed above i.e:

$\textcolor{#FF7968}{x}\text{\textcolor{#FF7968}{ = -3}}$

The operation of evaluating a function can be summarized as a substitution of the input value in the function's relationship and simplifying the result as follows:

$\begin{gathered} f\text{ ( -3 ) = -8}\cdot(-3)\text{ -9} \\ f\text{ ( -3 ) = 24 - 9} \\ \textcolor{#FF7968}{f}\text{\textcolor{#FF7968}{ ( -3 ) = 15}} \end{gathered}$

The above result of the function evaluation is as follows:

$\textcolor{#FF7968}{15}$