ACT Math · Function notation and transformations
A shipping company charges 5 for packages weighing 2 pounds or less, and 5 plus $1.50 per pound over 2 pounds for heavier packages. What…
A shipping company charges $5 for packages weighing 2 pounds or less, and $5 plus $1.50 per pound over 2 pounds for heavier packages. What is the cost to ship a 5-pound package?
Answer and explanation
Answer: D: $9.50
The package weighs pounds, which is more than pounds, so use the second rule: $5 plus $1.50 for each pound over . The excess is pounds, so the cost is dollars, choice D. Choice B ($12.50) applies the $1.50 rate to all pounds, , instead of just the excess. Choice A ($7.50) is with no base fee. Choice C ($11.00) comes from charging for extra pounds. Piecewise cost rules charge the per-pound rate only on the part above the threshold.
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- Question 19If f(x) = (3x-5)/(2), what is f^-1(7)?
- Question 20The function f(x) = -2(x-3)² + 7 has its vertex at (3, 7). What is f(5)?
- Question 55A function is defined by the table below. If the pattern continues, what is f(6)?
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