Answer:
[tex]y=2\sqrt[3]{x-0.5}+2[/tex]
Step-by-step explanation:
The translated form of a cube root function is:
[tex]y=a\sqrt[3]{x-h}+k[/tex]
where:
- a stretches or compresses the graph, and reflects it about the x-axis if a < 0.
- (h, k) is the point of inflection where the concavity of the function changes.
The parent function y = ∛x has a point of inflection at the origin (0, 0).
- Horizontal Shift: Shifting x by h moves the inflection point horizontally from (0, 0) to (h, 0).
- Vertical Shift: Shifting y by k moves the inflection point vertically from (h, 0) to (h, k).
In this case, the point of inflection of the dashed curve y = 2∛x is the origin (0, 0), and the point of inflection of the solid curve is (0.5, 2). Therefore:
So, the equation of the solid curve is:
[tex]\Large\boxed{\boxed{y=2\sqrt[3]{x-0.5}+2}}[/tex]
