Question

The function g is defined as follows for the domain given.

g(x)=2x-2, domain = {-3, -2, 1, 5)
Write the range of g using set notation. Then graph g.

Answer 1

1. range = {-8,-6,0,8}

2. My graph is attached to this response as a photo.

Explanation:

1. ⭐What is the "domain" of a function?

• Domain is another word for the x-values

⭐What is the "range" of a function?

• Range is another word for the y-values

⭐What is the "set notation"?

• Set notation is a way you can list numbers, such as x-values and y-values.
• When writing in set notation, you must list the numbers from least to greatest.

Therefore, we have to find the corresponding y-values for the given x-values, and then write said y-values in set notation.

To find the corresponding y-values for the given x-values, substitute each given x-value into g(x) and solve for g(x).

✦ When x = -3

`g(x) = 2x-2`

`g(-3) = 2(-3) -2`

`g(-3) = -6 -2`

`g(x) = -8`

✧ y = -8

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✦ When x = -2

`g(-2) = 2(-2) -2`

`g(-2) = -4-2`

`g(-2) = -6`

✧ y = -6

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✦ When x = 1

`g(1) = 2(1) -2`

`g(1) = 2-2`

`g(1) = 0`

✧ y = 0

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✦ When x = 5

`g(5) = 2(5) -2`

`g(5) = 10 -2`

`g(5) = 8`

✧ y = 8

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Next, we have to write the y-values in set notation. Make sure to write it from least to greatest.

range = {-8, -6, 0, 8}