Math Problem Statement
Solution
The question shown in the image asks to graph the function using transformations of the cube root function . Let's go through the steps needed to analyze and select the correct graph.
Function Breakdown:
- The base function is , which is the cube root function.
- The transformation involved is a vertical translation downward by 5 units. This is due to the "-5" outside the cube root, meaning the entire graph of is shifted down.
Steps to graph:
- Base Function: Start with the graph of . This function passes through the origin (0,0), and its general shape is an increasing curve.
- Vertical Shift: Subtracting 5 from shifts every point on the graph of downward by 5 units. So, instead of passing through (0,0), the graph now passes through (0, -5).
Now, check the graphs in the provided options:
- We are looking for the cube root graph, which has been shifted down by 5 units.
From the options:
- Option A: Shows a curve with the right behavior, starting at (0, -5).
- The other options (B, C, D) either do not shift downwards correctly or have a different behavior.
Thus, Option A is the correct graph.
Would you like any further details about graphing transformations?
5 Related Questions:
- How do horizontal translations affect the graph of a function?
- What is the difference between vertical and horizontal shifts in graphing?
- How does scaling (stretching or compressing) affect the graph of a cube root function?
- How do you find the domain and range of cube root functions?
- How would adding a coefficient to affect the graph?
Tip:
When graphing transformations, always start by analyzing the base function's key points and behavior before applying shifts or stretches!
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Algebra
Transformations of Functions
Cube Root Functions
Formulas
g(x) = ³√x - 5
f(x) = ³√x
Theorems
Vertical Translation
Suitable Grade Level
Grades 9-11
Related Recommendation
Graphing and Transforming Cube Root Function g(x) = 3√x + 5
Graphing the Transformation of Square Root Function g(x) = (1/3)√(x - 5)
Graphing Translated Square Root Function g(x) = √(x + 5)
Graphing the Function g(x) = 2 * cube root(x) with Transformations
Graphing the Transformation of Square Root Function g(x) = 1/3 √(x - 5)