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)
Responses

y=2x+1−−−−−√3−3
y equals 2 root index 3 Start Root x plus 1 End Root minus 3

y=x−1−−−−−√3+3
y equals root index 3 Start Root x minus 1 End Root plus 3

y=x+1−−−−−√3−3
y equals root index 3 Start Root x plus 1 End Root minus 3

y=2x−1−−−−−√3+3
y equals 2 root index 3 Start Root x minus 1 End Root plus 3

Answer 1

y = 2·∛(x − 1) + 3

Reason: A cube-root function of form y = a·∛(x − h) + k has a vertical tangent at x = h, so h = 1 and k = 3. Using (0,1): 1 = a·∛(−1) + 3 = −a + 3, so a = 2. Thus y = 2∛(x − 1) + 3 (the fourth choice).