A company awards its salespeople 3% commission on sales below $20,000, 3.5% commission on sales from $20,000 to $30,00, and 4% commission for sales over $30,000. Select the piecewise function that shows the commission for x dollars in sales. (1 point)

To determine the correct piecewise function for the commission based on the sales, we analyze the commission rates given for the different ranges of sales:

1. For sales below $20,000, the commission rate is 3%, which can be written as \( 0.03x \).
2. For sales from $20,000 to $30,000 (inclusive of $20,000 and $30,000), the commission rate is 3.5%, or \( 0.035x \).
3. For sales over $30,000, the commission rate is 4%, or \( 0.04x \).

Now we can create the piecewise function:

• For \( 0 \leq x < 20,000 \): \( f(x) = 0.03x \)
• For \( 20,000 \leq x \leq 30,000 \): \( f(x) = 0.035x \)
• For \( x > 30,000 \): \( f(x) = 0.04x \)

The correct piecewise function that represents this situation is:

\[ f(x) = \begin{cases} 0.03x & 0 \leq x < 20,000 \ 0.035x & 20,000 \leq x \leq 30,000 \ 0.04x & x > 30,000 \end{cases} \]

So, the correct response would be:

f⎛⎝⎜x⎞⎠⎟=⎧⎩⎨⎪⪪0.03x,0.035x,0.04x,0≤x<20,00020,000≤x≤30,000x>30,000⎞⎠⎟.