How do you determine the domain of a function?
In general, you want to look for x-value that are cannot exist for the function. Usually you want to find the values for x that would lead to a denominator of 0 if it is in fraction form, or if there is a square root, you can find the values of x that would lead to a negative number within the radical. Another case would be x-values that lead to negative numbers in log functions. These x-values would not be part of the domain. Everything other real number will be in the domain.
How do you determine where a function is discontinuous?
A function is discontinuous at a certain point if the value of the limit as the x-value approaches that point is different from the y-value at the point. In other words, if you plug in a specific x-value into the function and also find the limit of that x-value, if they are different, then the function is not continuous at that x-value. On a graph, discontinuities appear as holes, which are removable discontinuities, large gaps, and asymptotes, which are both non-removable discontinuities.
What happens to the market for iPods if household income decreases? Assume that iPods are a normal good.
Since iPods are a normal good, a decrease in income will lead to a decrease in demand for iPods, which shifts the demand curve to the left. This causes the equilibrium to move down and to the left, which causes a decrease in both price and quantity of iPods.