Hello!
1. Identify the parent function and its transformations
This graph is an example of a cube root function. Cubed root function act differently from squared root function. You can't square root a negative number, but you can with cube roots. That uniqueness causes this graph.
Parent function: [tex] y =\sqrt[3]{x} [/tex]
Looking at the graph, is shifted up one unit. Why? Let's substitute zero into the parent function:
y = ∛0 = 0
The parent function would have the point at (0, 0), while this graph is at (0, 1).
Also, the graphed is reflected over the x-axis because the graph is not increasing, but decreasing.
Answers:
- A reflection in the x-axis (first choice)
- A vertical shift of one unit upward (fifth choice)
2. Write an equation
Given the transformations, the graph is multiplied by -1, (reflection) and outside of the radicand, it is adding 1 (vertical shift)
y = [tex] -\sqrt[3]{x} + 1 [/tex]
Final answers:
- Parent function: [tex] y=\sqrt[3]{x} [/tex],
- Transformations: a reflection in the x-axis (choice 1), a vertical shift of one unit upward (choice 5)
- Graphed function: [tex] y=\sqrt[3]{x} + 1 [/tex]
