Question

The curve starts at left parenthesis 0 comma 1 right parenthesis and curves upward to the right to become vertical at left parenthesis 1 comma 3 right parenthesis. From that point the curve turns upward and rightward again to end at left parenthesis 2 comma 5 right parenthesis.

Sam graphed a cube root function. What is the equation of the function Sam graphed?

(1 point)

y=x+1−−−−−√3−3


y=x−1−−−−−√3+3


y=2x+1−−−−−√3−3


y=2x−1−−−−−√3+3

Answer 1

y = 2∛(x − 1) + 3

Reason: A cube-root has a vertical tangent (inflection) at its center, so use y = a∛(x − 1) + 3. Plugging (2,5) gives 5 = a·1 + 3 so a = 2. Check (0,1): 2∛(−1)+3 = 2(−1)+3 = 1. Thus the graph is y = 2∛(x − 1) + 3 (option 4).