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 = 2 x − 1 + 3
−−−−− √
3
y = x − 1 + 3 −−−−− √
3
y = x + 1 − 3
−−−−− √
3
y = 2 x + 1 − 3

Answer 1

A cube-root function has the form y = a ∛(x − h) + k, and a vertical tangent occurs at (h,k). Since the curve is vertical at (1,3), h = 1 and k = 3, so y = a ∛(x − 1) + 3. Use (2,5): 5 = a·∛1 + 3 ⇒ a = 2. So the equation is

y = 2 ∛(x − 1) + 3.