Question 1096558
<br>Let's look at your answer for part c first.<br>
You correctly found the slope by dividing the change in value by the number of years; the slope is -12,860.  That means the value is decreasing by $12,860 each year.  Then you found out how much the value would decrease over a 5 year period, and you subtracted that amount from the original value.  Exactly right.<br>
So you are good on part c.<br>
Now go back to part a.  The function you show suggests that the entire depreciation occurs in 1 year.  What you want in your function is the slope you calculated in part c.  So<br>
{{{f(x) = -12860x + 159500}}}<br>
Note that this is the standard "y=mx+b" form of the equation.  It is called standard form because it is the form that makes it easiest to use the equation in calculations.  But for a final answer to a question like this, a better form might be<br>
{{{f(x) = 159500 - 12860x}}}<br>
because then it is easier to see that the meaning of the function is that the initial value if $159,500 and then the value decreases by $12,860 each year.<br>
And finally part b.<br>
Note that the domain is the set of x values, not the set of y (function) values.  Since the problem says the machine is considered scrap after 9 years, the domain is from 0 to 9.<br>
The answer you tried to give for this part is the range (set of y values).  And again, since the machine is considered scrap after 9 years, the range would be from $43,760 to $159,500, not 0 to $159,500.<br>
And technically, in mathematics when we state the range, we always go from lowest y value to highest, as in the previous paragraph.  But in this problem, speaking informally, it would make sense to say the range is from 159,500 to 43,760.