Answer:
See the answers bellow
Explanation:
For 51:
Using the definition of funcion, given f(x) we know that different x MUST give us different images. If we have two different values of x that arrive to the same f(x) this is not a function. So, the pair (-4, 1) will lead to something that is not a funcion as this would imply that the image of -4 is 1, it is, f(-4)=1 but as we see in the table f(-4)=2. So, as the same x, -4, gives us tw different images, this is not a function.
For 52:
Here we select the three equations that include a y value that are 1, 3 and 4. The other values do not have a y value, so if we operate we will have the value of x equal to a number but not in relation to y.
For 53:
As he will spend $10 dollars on shipping, so he has $110 for buying bulbs. As every bulb costs $20 and he cannot buy parts of a bulb (this is saying you that the domain is in integers) he will, at maximum, buy 5 bulbs at a cost of $100, with $10 resting. He can not buy 6 bulbs and with this $10 is impossible to buy 0.5 bulbs. So, the domain is in integers from 1 <= n <= 5. Option 4.
For 54:
As the u values are integers from 8 to 12, having only 5 possible values, the domain of the function will also have only five integers values, With this we can eliminate options 1 and 2 as they are in real numbers. Option C is the set of values for u but not the domain of c(u). Finally, we have that 4 is correct, those are the values you have if you replace the integer values from 8 to 12 in c(u). Option 4.