Question

the table shows the daily pay in dollars, \\(f(x)\\), earned by a salesperson who makes \\(x\\) number of sales.

choose the function that represents the data.

\\(f(x) = 50x^2 + 200\\)
\\(f(x) = x^{50} + 200\\)
\\(f(x) = \frac{x}{50} + 200\\)
\\(f(x) = 50x + 200\\)

Explanation:

Determine the rate of change

$$ m = \frac{f(1) - f(0)}{1 - 0} = \frac{250 - 200}{1} = 50 $$

Identify the initial value

$$ f(0) = 200 $$

Formulate the linear equation

$$ f(x) = 50x + 200 $$

Answer:

• \(f(x) = 50x^2 + 200\)
• \(f(x) = x^{50} + 200\)
• \(f(x) = \frac{x}{50} + 200\)
• \(f(x) = 50x + 200\) (Correct answer)