Final answer:
The domain is all non-negative integers since texts are counted as whole numbers, and the range is all real numbers starting at $10, increasing in $0.10 increments after 1000 texts.
Step-by-step explanation:
The question asks us to find the domain and range for a cell phone plan that charges a flat fee and a variable fee for texts over a certain threshold. In this case, the plan costs $10 for up to 1000 texts, and $0.10 for each additional text beyond 1000. The domain of this function represents the number of texts sent and would be all non-negative integers, as you cannot send a negative number of texts and texts are usually counted in whole numbers. Hence, the domain is x ∈ I , where 'I' stands for the set of integers.
The range refers to the possible total costs. For up to 1000 texts, the cost is flat at $10. For each text over 1000, the cost increases by $0.10, so the range starts at $10 and increases in increments of $0.10. Therefore, the range is y ≥ 10, where 'R' stands for the set of real numbers since the cost is a continuous variable, represented in dollars and cents.For the domain, the number of texts can be any non-negative integerFor the range, the cost is $10 for up to 1000 texts. For any number of texts over 1000, the cost is calculated by multiplying the number of additional texts by $0.10 and adding it to $10.So, the range is any non-negative real number greater than or equal to $10.