A used car salesperson is paid a commission of 25 dollar...

Name: Problem 110, Chapter 1: Algebra and Trigonometry
Uploaded: 2020-11-22T18:43:29-08:00
Duration: 2 min 29 s
Channel: Kirsten Bauck
Description: A used car salesperson is paid a commission of 25 dollar plus 40 dollar of the selling price in excess of owner's cost. The owner claims that used cars typically sell for at least owner's cost plus 200 dollar and at most owner's cost plus 3000 dollar. For each sale made, over what range can the salesperson expect the commission to vary?

A used car salesperson is paid a commission of 25 dollar plus 40 dollar of the selling price in excess of owner's cost. The owner claims that used cars typically sell for at least owner's cost plus 200 dollar and at most owner's cost plus 3000 dollar. For each sale made, over what range can the salesperson expect the commission to vary?

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Key Concepts

Applied Function Evaluation

Applied function evaluation refers to substituting particular values into a linear expression to get the resultant output. In contexts like commission calculations, by plugging the extreme values of the input variable into the function, one can determine the minimum and maximum achievable outcomes for the commission.

Linear Function

A linear function represents relationships where one quantity changes at a constant rate with respect to another. In many real world scenarios, such as commission calculations, the relationship between variables (for example, sales price and commission earned) can be expressed in the form f(x) = mx + b, where m represents the rate of change and b is the fixed base amount.

Domain and Range Analysis

This concept involves understanding the set of possible input values (the domain) and the corresponding set of output values (the range) for a given function. When constraints are applied to the inputs—such as specifying a minimum and maximum selling price—the output, such as the commission, will be limited to a specific interval determined by evaluating the function at these boundaries.

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