ID: af2ba762
(SAT Suite Question Bank > Find Questions > Assessment: SAT + Test: Math + Domain: Algebra)
Comment: Pay close attention to what is inside the parentheses. Consider what the equation is actually modeling.
Method 1: This question seems designed to catch the lazy or absent-minded student who sees x months after September 1 and takes a cursory glance at the given equation:
F(x) = 2.74 - 0.19(x - 3)
So, if the question asks about the constant 2.74, and that constant is found in the "starting value" position above, many students will assume that 2.74 is the [average] price per gallon of fuel on September 1 and select (C). However, we have to wonder why the part in parentheses is not just x, but x - 3. If (C) were correct, then what, exactly, does x - 3 mean? 0 months after September 1? But then that would lead to a different price:
F(x) = 2.74 - 0.19((0) - 3)
F(x) = 2.74 - 0.19(-3)
F(x) = 2.74 + 0.57
F(x) = 3.31
It would seem that the price was $3.31 per gallon on September 1, not $2.74, as the answer choice says. In short, (C) cannot be correct. (It is impossible for the average price to have been two separate numbers simultaneously.)
To zero out the part in parentheses, x must be 3, rather than 0, and since x represents the number of months after September 1, 3 months later would be December 1: Sept-Oct-Nov-Dec. Thus, the correct answer is (D).
Method 2: There is nothing wrong with graphing the equation in Desmos, especially because the numbers are so small. You would still need to think about what the graph actually meant, though.
It is not necessary to input the function as F(x)—you could just use y. But if you are a purist, click on the large + button, "Add Item," in the top-left corner of the screen and select "f(x) expression." For the table, click on the gear icon, "Edit List," above the equation, then fill in the points 0 through whatever until the table derives the value 2.74. You could also use a slider on the line to get to 2.74. In any case, the correct x-value is clearly 3, and once again, 3 months after September 1 means December 1, and the correct answer is (D).
Method 3: You could work to disprove the incorrect answer choices in an effort to increase your confidence in your eventual answer. (A) makes no sense because an average decrease would be a rate—a change or, in linear terms, a slope—and the number 2.74 would have to be attached to x for this to be an accurate statement. As for (B), any difference between months would have to be derived from plugging in values to the equation itself. You could even test 3 (for December) and 0 (for September), respectively, to check. We already know that x = 0 will yield a value of 3.31 for F(x), as shown above. Plugging in 3 for x will cancel out the part in the parentheses, as discussed earlier but not actually shown.
F(3) = 2.74 - 0.19((3) - 3)
F(3) = 2.74 - 0.19(0)
F(3) = 2.74 - 0
F(3) = 2.74
Subtracting 2.74 from 3.31 does not yield 2.74, needless to say, so (B) cannot be correct either. (C) and (D) I have covered extensively in method 1 above, so I will avoid a recapitulation here. Although this method is not the most efficient, and adding steps will only increase the probability of making a mistake somewhere, it can nevertheless be an effective way to arrive at an accurate answer, which is the ultimate goal however you look at it.
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