Question

Find the range of the function for the given domain.

Answer 1

Answer:  D.  {-12, -9, -6, -3, 0}

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Explanation:

The domain is the set of allowed x inputs. The range is the set of possible y outputs.

The set {-2,-1,0,1,2} represents all the possible x inputs

Let's plug each of those into the equation y = 3x-6 to find the corresponding paired out puts.

Note: y = f(x), so f(x) = 3x-6 is the same as y = 3x-6.

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If x = -2, then,

y = 3x-6

y = 3(-2)-6

y = -6-6

y = -12

We see that x = -2 and y = -12 pair up together.

The value -2 in the domain maps to -12 in the range.

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If x = -1, then,

y = 3x-6

y = 3(-1)-6

y = -3-6

y = -9

The input x = -1 in the domain maps to the output y = -9 in the range

So far the range consists of {-12, -9} in either order.

The answer is between A and D

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If x = 0, then,

y = 3x-6

y = 3(0)-6

y = 0-6

y = -6

So -6 is also part of the range. We have {-12, -9, -6} so far. The answer is still between A and D.

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If x = 1, then,

y = 3x-6

y = 3(1)-6

y = 3-6

y = -3

The range updates to {-12, -9, -6, -3}

A and D are still equally valid

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We have one more x value to try

If x = 2, then,

y = 3x-6

y = 3(2)-6

y = 6-6

y = 0

Since y = 0 is in the range, instead of y = 1, this rules out choice A

The answer is therefore D.  {-12, -9, -6, -3, 0}