Question

A piecewise function f(x) is defined as shown.

f(x) = StartLayout enlarged left-brace 1st Row 1st column negative five-fourths x + 90, 2nd column 0 less-than-or-equal-to x less-than 40 2nd row 1st column negative three-eighths x + 75, 2nd column 40 less-than-or-equal-to x less-than-or-equal-to 200 EndLayout

Which table could be used to graph a piece of the function?

A 2-column table has 3 rows. The first column is labeled x with entries 0, 16, 40. The second column is labeled y with entries 90, 85, 75.

A 2-column table has 3 rows. The first column is labeled x with entries 0, 40, 200. The second column is labeled y with entries 90, 40, 0.

A 2-column table has 3 rows. The first column is labeled x with entries 40, 120, 200. The second column is labeled y with entries 75, 30, 0.

A 2-column table has 3 rows. The first column is labeled x with entries 40, 160, 200. The second column is labeled y with entries 60, 15, 0.

Answer 1

D

Check the second piece f(x) = -(3/8)x + 75 (valid for 40 ≤ x ≤ 200):
- f(40) = 75 - (3/8)(40) = 75 - 15 = 60
- f(160) = 75 - (3/8)(160) = 75 - 60 = 15
- f(200) = 75 - (3/8)(200) = 75 - 75 = 0

These match the table in choice D.