Question

identify the following function:

○ square root function
○ cubic function
○ cube root function
○ quadratic function

Explanation:

1. A square root function $y=\sqrt{x}$ only exists for $x\geq0$ and has a vertical tangent at its starting point, which does not match the graph's shape and domain.
2. A cubic function $y=ax^3+bx^2+cx+d$ is a smooth, unbounded curve that extends to both positive and negative infinity without a "corner" shape, which does not match the graph.
3. A cube root function $y=\sqrt[3]{x-h}+k$ has a characteristic "corner" (a point where the derivative is undefined) and is defined for all real numbers, matching the shape and behavior of the given graph.
4. A quadratic function $y=ax^2+bx+c$ is a parabola (U-shaped or downward U-shaped), which does not match the graph's shape.

Answer:

C. CUBE ROOT function