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Answer:
- C. (-∞, -2)∪(-2, 1)∪(1, ∞)
- A. The first 12 are $2 ea; $1 ea after
Step-by-step explanation:
1. The denominator in the first part of the function definition factors as ...
x² +x -2 = (x -1)(x +2)
This has zeros at x = -2 and x = 1, which will be values of x excluded from the domain. (These zeros are in the domain x < 2, which is applicable to this part of the function definition.)
The second part of the function definition is defined for all x ≥ 2, so the only exclusions are x = -2 and x = 1. The domain of the piecewise function is ...
(-∞, -2)∪(-2, 1)∪(1, ∞)
__
2. It is helpful to take a look at the graph to see what the axis labels are. The x-axis is labeled "number of cupcakes", so "12" on that axis means "12 cupcakes". The y-axis is labeled "total cost", which we are to presume is in dollars. That means the slope of the graph is Δy/Δx = "dollars per cupcake", the cost of one cupcake.
We observe that the slope of the graph decreases at x=12. This means the cost of a cupcake goes down after 12 are purchased. The appropriate description is ...
The first 12 cupcakes cost $2 each, and all cupcakes after that cost $1 each.
(The other choices have either increasing slope at the breakpoint, or a different breakpoint, or both, so cannot be right.)
