A gas tank can hold 12 gallons of gas. The equation \( p(g)=3.5 g \) gives the amount of money it costs when filling the tank with gas. What is the range for this situation? \( \{0,1,2,3, \ldots, 42\} \) \( \{3.50,7,10.50,14, \ldots 42\} \) \( \{p(g) \mid 0 \leq p(g) \leq 42\} \) \( \{p(g) \mid p(g) \leq 42\} \)

To determine the **range** of the function \( p(g) = 3.5g \) given that the gas tank can hold up to **12 gallons**, let's analyze the situation step-by-step. ### Understanding the Function - **Function:** \( p(g) = 3.5g \) - Here, \( p(g) \) represents the cost in dollars. - \( g \) represents the number of gallons of gas. - **Domain:** Since the gas tank can hold a maximum of 12 gallons, \( g \) can range from **0 to 12**. - \( 0 \leq g \leq 12 \) ### Calculating the Range - **Minimum Cost:** When \( g = 0 \) gallons, \[ p(0) = 3.5 \times 0 = \$0 \] - **Maximum Cost:** When \( g = 12 \) gallons, \[ p(12) = 3.5 \times 12 = \$42 \] - **Intermediate Costs:** For any value of \( g \) between 0 and 12, \( p(g) \) will yield a cost between \$0 and \$42. Since \( g \) can take any real number within this interval, the costs are **continuous** and not just discrete values. ### Evaluating the Options 1. **\( \{0,1,2,3, \ldots, 42\} \):** - **Incorrect.** This suggests only integer dollar amounts, ignoring the continuous nature of gas measurements. 2. **\( \{3.50,7,10.50,14, \ldots, 42\} \):** - **Incorrect.** This lists specific multiples of \$3.50, excluding other possible values. 3. **\( \{p(g) \mid 0 \leq p(g) \leq 42\} \):** - **Correct.** This accurately represents all possible costs from \$0 to \$42, inclusive. 4. **\( \{p(g) \mid p(g) \leq 42\} \):** - **Partially Correct but Incomplete.** While it includes all costs up to \$42, it doesn't specify the lower bound (which is \$0). ### **Conclusion** The **range** of the function is best represented by: **\( \{p(g) \mid 0 \leq p(g) \leq 42\} \)** This option accurately captures all possible cost values from \$0 up to \$42, considering the continuous nature of gas measurements. **Answer:** \(\{p(g) \mid 0 \leq p(g) \leq 42\}\)