1) A function is a relationship between an input and an output. One of the rules of functions is that for each input, you can only have one output. Say the x value = your input and the y value = your output. For every x-value, you can only have one y-value.
You can use the vertical line test for this. If you move a vertical line across the graph of a function, it cannot cross the graph in more than one place (see picture).
For this problem, if there are ordered pairs with same x-value that have different y-values, then it can't be a function. Notice that (-1, 9) and (-1, -9) have the same x-value, but different y-values. They break the vertical line rule.
Answer: Not a function. (-1, 9) and (-1, -9) break the rule.
2) The domain is the set of x-values for a function. The range is the set of y-values for a function. You're given -3, -1, and 6 as the set of values for the domain. That means -3, -1, and 6 are the x-values you plug into the function to find y. Remember that "f(x)" is the same thing as saying "y."
So your function is:
f(x) = 12 - 3x+2 x^{2}
Plug in x=-3, x=-1, x=6:
f(-3) = 12 - 3(-3)+2 (-3)^{2} = 12 + 9+18=39
f(-1) = 12 - 3(-1)+2 (-1)^{2} = 12+3+2=17
f(6) = 12 - 3(6)+2 (6)^{2}=12-18 + 72 = 66
So your y-values are 39, 17, and 66, in that order. Since the range is the set of y-values for a function, your answer is Range: {39, 17, 66}
3) In a sequence, n = the term number, making f(x) the term value. That means to find the value of terms 1, 2, and 3, you simply need to put those numbers into the function as n to find f(x).
Your function is:
f(x)=38-3(n-1)
Plug in 1, 2, and 3:
f(x)=38-3(1-1) = 38-3(0)=38\\ f(x)=38-3(2-1) = 38-3(1)=35\\ f(x)=38-3(3-1) = 38-3(2)=32
For term #1, the term value = 38
For term #2, the term value = 35
