Question

Find the range of the function for the given domain.

f(x) = 3x -6;{-2,-1,0,1,2}

What is the range? Choose the correct answer below.

A. {-13, - 9,-6,-3,1)

B. {-12, - 8,-6,- 2,0}

C. {-12, - 8, -7,-2,0)

D. {-12,-9,-6,-3,0}

Answer 1

The range of the function f(x) = 3x - 6 for the given domain is {-12, -9, -6, -3, 0}.

Step-by-step explanation:

The range of a function represents the set of all possible output values of the function. To find the range of the function f(x) = 3x - 6, we need to evaluate the function for each value in the given domain and determine the set of corresponding output values.

For the given domain {-2, -1, 0, 1, 2}, we substitute each value into the function:

f(-2) = 3(-2) - 6 = -12

f(-1) = 3(-1) - 6 = -9

f(0) = 3(0) - 6 = -6

f(1) = 3(1) - 6 = -3

f(2) = 3(2) - 6 = 0

Therefore, the range of the function f(x) = 3x - 6 for the given domain is {-12, -9, -6, -3, 0}.

Answer 2

Answer: D. {-12, -9, -6, -3, 0}

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Step-by-step 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}