The graph below represents the total amount of chips in the bag in oz., y, over
time, x, in minutes.
x+2y=7
(7.0) x
6.
6
(0,3.5)
2
4-2 0 24
-2
4
9
-6
8
Figure 1
(7.0) x
1) What is the end behavior of the graph?
2) What would be a reasonable domain (input) for this scenario?
3) What would be reasonable range (outputs) for the scenario?
End Behavior
As x goes to -∞, y goes to -∞. As x goes to
+∞, y goes to ∞o.
As x goes to -∞, y goes to +∞. As x goes to
+∞, y goes to -∞.
Reasonable domain
:: [0, 3.5] :: [0,7]
Reasonable outputs
:: [0,3.5] :: [0,8] :: [0,7]
Based on the equation x + 2y = 7, the graph shows a linear relationship between x and y where the total amount of chips in the bag in ounces is represented by y and time in minutes is represented by x.
1) The end behavior of the graph shows that as x approaches -∞, y also approaches -∞ and as x approaches +∞, y approaches +∞. This indicates that as more time passes, the total amount of chips in the bag increases.
2) A reasonable domain for this scenario would be from 0 to 7, as the total amount of chips in the bag cannot be negative and cannot exceed 7 ounces.
3) A reasonable range for this scenario would be from 0 to 3.5, as the total amount of chips in the bag cannot be negative and cannot exceed 3.5 ounces at any given time.