Analyzing Functions in Context

a

Let's consider the given function. $C = - 4 m + 15$ In the above formula, $C$ is the number of cylinders Ralph has left after finishing his work on $m$ engines. Since the number of cylinders remaining, $C,$ depends on the number of motors, $m,$ we can say that $C$ is the dependent variable and $m$ is the independent variable.

b

To determine the range of the function, we can substitute the given domain values into the equation and simplify.

$m$	$- 4 m + 15$	$C$
$0$	$- 4 \cdot 0 + 15$	$15$
$1$	$- 4 \cdot 1 + 15$	$11$
$2$	$- 4 \cdot 2 + 15$	$7$
$3$	$- 4 \cdot 3 + 15$	$3$

From the table above, we can identify the $C$ -values in the range that correspond to the $m$ -values in the domain. $R : {3, 7, 11, 15}$

Analyzing Functions in Context 1.6 - Solution