https://file.aiquickdraw.com/mathbot/file/1727201492159b9soqxhb.jpg

The problem asks for the equation of the blue graph \( G(x) \), which is stated to have the same shape as the red graph \( F(x) = x^3 \). This implies that \( G(x) \) is a transformation of \( F(x) \), specifically a horizontal shift, since the two graphs appear identical except for their position along the x-axis.

### Analysis:
1. The red graph \( F(x) = x^3 \) passes through the origin, whereas the blue graph \( G(x) \) seems to have the same shape but is shifted left.
2. A horizontal shift of a cubic function \( x^3 \) can be described by \( G(x) = (x - h)^3 \), where \( h \) is the shift. From the graph, it appears the blue graph is shifted 3 units to the left, which gives the equation:
   \[
   G(x) = (x + 3)^3
   \]

### Conclusion:
The equation of the blue graph is \( G(x) = (x + 3)^3 \), which corresponds to option **C**.

Let me know if you want more details or have any questions! Here are five follow-up questions related to this topic:

1. How does a horizontal shift affect the graph of a function?
2. What is the difference between horizontal and vertical shifts in transformations?
3. How can you identify a vertical shift from a graph?
4. What happens to the graph of \( f(x) = x^n \) when you apply a reflection over the y-axis?
5. Can you describe how other types of transformations (like stretching or compressing) would modify the graph of \( x^3 \)?

**Tip:** When analyzing graph transformations, always look at the vertex (or the key point) and check if the movement is horizontal, vertical, or both.

The graphs below have the same shape. What is the equation of the blue graph? Given F(x) = x^3.

Learn how to identify the equation of a cubic function that has undergone a horizontal shift. This example focuses on shifting the graph of F(x) = x^3 and determining the new function. Suitable for students in Grades 9-11.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation