Question
Describe the transformation from \( v(x)=x^{3}+2 \) to \( q(x)=(0.25 x)^{3}+2 \). 1 point horizontal stretch by a factor of 0.25 horizontal compression by a factor of 4 horizontal stretch by a factor of 4 horizontal compression by a factor of 0.25
Ask by Greene Mckenzie. in the United States
Jan 23,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The transformation is a horizontal stretch by a factor of 4.
Solution
The transformation from \( v(x) = x^3 + 2 \) to \( q(x) = (0.25x)^3 + 2 \) involves a horizontal scaling.
When the input \( x \) is multiplied by 0.25, it results in a horizontal stretch by a factor of \( \frac{1}{0.25} = 4 \).
**Answer:**
**horizontal stretch by a factor of 4**
Reviewed and approved by the UpStudy tutoring team
Like
error msg
Explain 
Simplify this solution Bonus Knowledge
The transformation from \( v(x)=x^{3}+2 \) to \( q(x)=(0.25 x)^{3}+2 \) involves a horizontal compression by a factor of 4. This is because when you input \( 0.25 x \) into the function, it effectively speeds up how quickly the graph reaches its values compared to the original function. So, for every unit increase in \( x \), \( q(x) \) increases faster than \( v(x) \). In simpler terms, you can think of it like this: by replacing \( x \) with \( 0.25 x \), you are really saying that the function will achieve the same output values much quicker, hence, making the graph "squeeze" towards the y-axis. It's like hugging your friends tighter at a group photo!
