Question

Joe is ordering greeting cards for the holidays. Pricing is based on how many cards he orders. The following piecewise function represents the cost for a bundle of cards and x represents the number of cards ordered.

f(x)=⎧⎩⎨⎪⎪1.5x if 1≤x<501.25x if 50≤x<75x if 75≤x<100


Which of the following points would have an open circle when graphed?

(1 point)

(50,75)


(60,90)


(50,62.5)


(75,75)

Answer 1

(50, 75)

Reason: The first piece 1.5x is defined for 1 ≤ x < 50, so at x = 50 that piece gives 1.5·50 = 75 but x = 50 is not included (open circle). The value at x = 50 is actually f(50) = 1.25·50 = 62.5 from the second piece, which is a filled point.