A hotel has a budget of $16,000 to buy 84 new mattresses. Each mattress costs $209. The hotel manager says, “Since 80 × $200 = $16,000, I can stay within the budget.”

The hotel manager under-estimated. Without estimation, the exact price would be $17,556.

Step-by-step explanation:

He should've over-estimated the money to $210, and the mattresses to 90.  So 210 × 90 is $18,900. So even if he did underestimate or overestimate, he still would not have been able to afford the mattresses.

horizontal translation of 2 units in the positive x direction

followed by

vertical translation of 3 units in the positive y direction