Question

HELP PLEASE MATH :((((

Answer 1

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: $y =\sqrt[3]{x}$

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 = $-\sqrt[3]{x} + 1$

Final answers:

1. Parent function: $y=\sqrt[3]{x}$,
2. Transformations: a reflection in the x-axis (choice 1), a vertical shift of one unit upward (choice 5)
3. Graphed function: $y=\sqrt[3]{x} + 1$