Question
If \( f(x)=x^{3} \), what is the effect on its graph when \( f(x) \) is replaced by \( f(-2 x) \) ? (1 point) a horizontal stretch and reflection over the \( y \)-axis a horizontal compression and reflection over the \( y \)-axis a vertical stretch and reflection over the \( x \)-axis a vertical compression and reflection over the \( x \)-axis
Ask by Huff Campos. in the United States
Jan 23,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The graph undergoes a horizontal compression and a reflection over the \( y \)-axis.
Solution
When \( f(x) \) is replaced by \( f(-2x) \), the transformation involves two main changes:
1. **Reflection over the \( y \)-axis**: The negative sign inside the function argument \( (-2x) \) causes a reflection across the \( y \)-axis.
2. **Horizontal Compression**: The factor of 2 inside the function argument compresses the graph horizontally by a factor of \( \frac{1}{2} \).
Therefore, the graph undergoes a **horizontal compression** and a **reflection over the \( y \)-axis**.
**Answer:**
a horizontal compression and reflection over the \( y \)-axis
Reviewed and approved by the UpStudy tutoring team
Like
error msg
Explain 
Simplify this solution Bonus Knowledge
When we replace \( f(x) \) with \( f(-2x) \), we are effectively substituting \( -2x \) into the function. This operation results in two transformations: the negative sign reflects the graph over the \( y \)-axis, while the factor of 2 compresses the graph horizontally by a factor of \( \frac{1}{2} \). Therefore, the correct answer is that there is a horizontal compression and reflection over the \( y \)-axis.
