Question

identifying domain & range;
12
domain
laurie has a $25 gift card to a
cafe. she is going to buy 1-3
sandwiches. the function
g(x) = 25 - 4x represents the
total cost, g(x), that it costs based
on the number of sandwiches, x,
bought. fill out the table for this
situation to help determine the
domain & range.
range:
(table with x and g(x) columns)
x = 1 then g(x) =
x = 2 then g(x) =
x = 3 then g(x) =
domain
range
options: $13, $21, $17, {1,2,3}, {13,17,21}, {3,2,1}, {21,17,13}

Explanation:

Step1: Calculate g(1)

Substitute \( x = 1 \) into \( g(x)=25 - 4x \). So \( g(1)=25 - 4(1)=25 - 4 = 21 \).

Step2: Calculate g(2)

Substitute \( x = 2 \) into \( g(x)=25 - 4x \). So \( g(2)=25 - 4(2)=25 - 8 = 17 \).

Step3: Calculate g(3)

Substitute \( x = 3 \) into \( g(x)=25 - 4x \). So \( g(3)=25 - 4(3)=25 - 12 = 13 \).

Step4: Determine Domain

The number of sandwiches \( x \) can be 1, 2, 3 (since she is buying 1 - 3 sandwiches as per the table filling for this situation), so domain is \( \{1, 2, 3\} \).

Step5: Determine Range

The corresponding \( g(x) \) values are 21, 17, 13, so range is \( \{13, 17, 21\} \) (or \( \{21, 17, 13\} \) as order doesn't matter for sets but matching the options).

Matching the options:

• \( x = 1 \) then \( g(x)=\$21 \)
• \( x = 2 \) then \( g(x)=\$17 \)
• \( x = 3 \) then \( g(x)=\$13 \)
• Domain: \( \{1, 2, 3\} \)
• Range: \( \{13, 17, 21\} \) (or \( \{21, 17, 13\} \) as one of the options is \( \{21, 17, 13\} \))

Answer:

• \( x = 1 \) then \( g(x) \): \(\boldsymbol{\$21}\)
• \( x = 2 \) then \( g(x) \): \(\boldsymbol{\$17}\)
• \( x = 3 \) then \( g(x) \): \(\boldsymbol{\$13}\)
• Domain: \(\boldsymbol{\{1, 2, 3\}}\)
• Range: \(\boldsymbol{\{21, 17, 13\}}\) (or \(\{13, 17, 21\}\) but matching the option \(\{21, 17, 13\}\))