Question
How does the graph of \( f(x)=\sqrt[3]{x} \) change when \( f(x) \) is replaced by \( f(7 x) \) ? (1 point) The graph moves down 7 units. The graph moves to the right 7 units. The graph moves up 7 units. The graph does not shift left or right.
Ask by Hobbs George. in the United States
Jan 23,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The graph does not shift left or right.
Solution
When you replace \( f(x) \) with \( f(7x) \), you're applying a horizontal scaling to the graph of \( f(x) = \sqrt[3]{x} \). Specifically, the graph is compressed horizontally by a factor of \( \frac{1}{7} \). This transformation does **not** move the graph left or right; it only changes its width.
**Answer:**
The graph does not shift left or right.
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Mind Expander
When you replace \( f(x) \) with \( f(7x) \), you're compressing the graph horizontally by a factor of 7. This means that for every value of \( x \), the corresponding output \( f(x) \) is achieved at \( 7x \) instead, effectively pulling the graph closer to the y-axis. So, it doesn’t move left or right at all; rather, it becomes more concentrated around the y-axis. To visualize it, think of it like squishing a sponge – the overall shape stays the same, but it gets narrower. So the correct answer here is that "The graph does not shift left or right."
