Hey CPhill I found a mistake with your graph which threw me off so I fixed it here: https://www.desmos.com/calculator/tqvci9lcnt
As you can see you are graphing the function from x = -2 to x = 4 and your graph had the signs facing the wrong way. Maybe you can look it over and fix (b), (c), and (d) in the problem which I think affects it from the mistake.
6. A player chooses one of the numbers 1 through 4. After the choice has been made, two regular four-sided (tetrahedral) dice are rolled, with the sides of the dice numbered 1 through 4. If the number chosen appears on the bottom of exactly one die after it has been rolled, then the player wins 1 dollar. If the number chosen appears on the bottom of both of the dice, then the player wins 2 dollars. If the number chosen does not appear on the bottom of either of the dice, the player loses 1 dollar. What is the expected return to the player, in dollars, for one roll of the dice?