Question

An alien planet uses a unique tax structure to tax its residents. For income less than $25,000, an alien pays a 5% tax. For income $25,000 or more, but less than $100,000, an alien pays $7500. For income of $100,000 or more, an alien pays a 12% tax.

Which piecewise function models the tax paid by an alien earning x dollars?

(1 point)

f(x)=⎧⎩⎨⎪⎪0.05x75000.12xififif0≤x<25,00025,000≤x<100,000x≥100,000


f(x)=⎧⎩⎨⎪⎪0.5x75000.12xififif0≤x<25,00025,000≤x<100,000x≥100,000


f(x)=⎧⎩⎨⎪⎪0.05x75000.12xififif0≤x≤25,00025,000<x<100,000x≥100,000


f(x)=⎧⎩⎨⎪⎪0.05x75000.12xififif0≤x<25,00025,000≤x<100,000x>100,000

Answer 1

The first option.

Reason: For 0 ≤ x < 25,000 tax = 5% → 0.05x; for 25,000 ≤ x < 100,000 tax = $7,500; for x ≥ 100,000 tax = 12% → 0.12x.