It's easier to sketch if you simplify . Factorize the numerator and denominator - simple to do with a difference of cubes or squares.
If , we can cancel the factors of . Note that itself is undefined. For all intents and purposes, aside from the singularity at , the graph of will look exactly like the graph of
Now, rewrite this as
Then when (note that is also undefined), we can cancel to reduce this to
On its own, the graph of is a line through the origin. When is a large number is small. But as gets closer to -1, the rational term blows up. Effectively, this means the graph of looks like around , and far enough away it looks like .
See the attached plot for a sketch of these details.
Step one, first we must find out if there is a pattern in the earnings column. so the numbers are 19,38,57,?,95. This case there is a pattern. It adds up 19 each time
Step two fin out what goes in the question mark. To do so we need to add 19+19=38 then 38+19=57 now we need to add 19+57 to get our missing number. The answer is 76
T( 1.50+ 1.25) + 10.00 < 20.00
2.75t + 10.00 < 20.00
2.75t < 10.00
T < 3.63
Partial bulbs and puts can't be bought, so Anika cannot spent the full $20.00.
Therefore, t < 3 if t can be a whole number.