Answer:
(1) <em>Observe the attached image</em>
(2) ![S = \$4,000](https://tex.z-dn.net/?f=S%20%3D%20%5C%244%2C000)
(3) ![x = \$90,000](https://tex.z-dn.net/?f=x%20%3D%20%5C%2490%2C000)
(4) ![S = 2100](https://tex.z-dn.net/?f=S%20%3D%202100)
Step-by-step explanation:
(1) Let's call S the salary for the month the seller wins.
Let's call x the amount of dollars reached by the sales of that month.
The seller earns a base salary of $ 2100 per month.
Then, if x> 42,000 he wins a commission of 5% on sales.
Then the equation modeling this situation is:
![S =\left\{{{0.05(x-42,000)+2100\ if\ x>42,000} \atop{2,100\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ if\ 0\leq x\leq42,000}}\right.](https://tex.z-dn.net/?f=S%20%3D%5Cleft%5C%7B%7B%7B0.05%28x-42%2C000%29%2B2100%5C%20if%5C%20x%3E42%2C000%7D%20%5Catop%7B2%2C100%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20if%5C%200%5Cleq%20x%5Cleq42%2C000%7D%7D%5Cright.)
<em>The graph of the function is shown in the attached image.
</em>
(2) If x = 80,000, then your salary was:
![S = 0.05(80000-42000) +2100\\\\S = \$4,000](https://tex.z-dn.net/?f=S%20%3D%200.05%2880000-42000%29%20%2B2100%5C%5C%5C%5CS%20%3D%20%5C%244%2C000)
(3) If S was 4500 and we want to find x then we equal S to 4500 and solve for x.
![S = 4,500 = 0.05(x-42,000) + 2,100\\\\\frac{2,400}{0.05} = (x-42,000)\\\\x = \frac{2400}{0.05} +42,000\\\\x = \$90,000](https://tex.z-dn.net/?f=S%20%3D%204%2C500%20%3D%200.05%28x-42%2C000%29%20%2B%202%2C100%5C%5C%5C%5C%5Cfrac%7B2%2C400%7D%7B0.05%7D%20%3D%20%28x-42%2C000%29%5C%5C%5C%5Cx%20%3D%20%5Cfrac%7B2400%7D%7B0.05%7D%20%2B42%2C000%5C%5C%5C%5Cx%20%3D%20%5C%2490%2C000)
(4) S (25000) means that x equals 25000. Since x represents sales, this means that during the month, the seller only reached $ 25,000.
Then ![x](https://tex.z-dn.net/?f=x%20%3C42000)
Therefore
.