Math Problem Statement
Solution
Let's go through this step-by-step to solve the given problem.
Given Function:
Part a: Parent Function
The function involves a cube root, so the parent function is:
Thus, the correct parent function is:
Part b: Reflections
There is no negative sign in front of the cube root, so there is no reflection.
Part c: Stretches/Compressions
The function does not have a coefficient multiplying , so there is no vertical stretch or compression.
Part d: Vertical Shifts
The function has added outside the cube root, which represents a vertical shift down by 3 units.
Part e: Horizontal Shifts
There is no transformation inside the cube root (i.e., no term added or subtracted from ), so there is no horizontal shift.
Summary:
- Parent function:
- Reflections: None.
- Stretches/Compressions: None.
- Vertical Shifts: Down 3 units.
- Horizontal Shifts: None.
Let me know if you'd like further details or have any questions.
Here are some related questions for practice:
- What would the transformation be if the function was ?
- How would a horizontal shift affect the function ?
- What is the difference between vertical and horizontal shifts?
- How would a coefficient in front of affect the graph?
- Can a cubic root function have a reflection and a vertical shift simultaneously?
Tip: Always check for transformations both inside and outside the root or any function to understand its graph!
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Transformations
Parent Functions
Shifts
Formulas
f(x) = ∛x - 3
Theorems
Transformation of Functions
Suitable Grade Level
Grades 9-12