Here the set of input values is {0, 1, 2, 3, 4} and the set of output values is {0, 4, 16, 36, 64).
Because of the rapid growth in the set of output values (0 to 4, 4 to 16, 16 to 36, 36 to 64), we suspect that exponential growth is illustrated here.
Let's start with the basic equation for exponential growth: f(x) = ar^(n-1), where a is the value of the first term, n is the subscript of the term in question (e.g., n = 2 would indicate the second term), r is the common factor (if there is one).
The first y-value is 0; the second is 4, and the third is 16. Is 4 a common ratio here? Multiplying the first y value (0) by 4 results in 0. Is that the same as the second given y-value (4)? No. So 4 is not a common ratio, even though 4 times 4 = 16 (the third y-value).
If you are in an advanced algebra class, one approach to try next would be to "fit" the given points to a 2nd, 3rd, 4th or 5th order polynomial. For example, we could begin with given point (1,4) and attempt a 2nd order (quadratic) fit to (1,4) as a first step towards finding the "rule" in question.
The general form of a quadratic function is y=ax^2+bx+c. What happens if we let x=1 and y=4, to fit (1,4)? y = 4 = a(1)^2 + b(1) + c, which has 3 unknown coefficients. You must repeat this process until you have three equations in three unknowns {a, b, c}, and then you must solve for a, b and c. If you do this properly, you'll end up with a quadratic formula for the "rule" in question.
I'd suggest you double-check to ensure that you have copied the five given data points properly.
7.42 as a fraction is 7420/1000. Now you need to simplify it. The easiest way to do this is to continuously divide the top and bottom by 2 as long as it is even. At this point it should be small enough to figure out the other factors, and finish simplifying it. This only simplifies to 371/50. While 371 is divisible by 7 and 53, 50 is not divisible by either of them, so the final solution is 371/30
Use each of the domain values in the function to see what the corresponding range value is.
f(-1) = 5 -3(-1) = 8
f(0) = 5 -3(0) = 5
f(2) = 5 -3(2) = -1
The range is the set of numbers {-1, 5, 8}.
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<em>Additional comment</em>
The values in a set are generally listed lowest to highest. The coefficient of x in the equation for f(x) is negative, meaning the lowest range value will correspond to the highest domain value. If you start by finding f(2) = -1, you immediately eliminate all answer choices except B and C.
Those choices differ only in the middle value, so you can tell which is correct by evaluating f(x) for the middle domain value: f(0) = 5. Only one answer choice has both -1 and 5 in the set.
(There are two answers here: how you work the problem, and how you game a multiple choice question.)
