Question
What is the effect on the graph of \( f(x)=\sqrt[3]{x} \) when \( f(x) \) is replaced by \( f(x-1) \) ? (1 point) The graph shifts up. The graph shifts right. The graph shifts left. The graph shifts down.
Ask by Luna Hammond. in the United States
Jan 23,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The graph shifts right.
Solution
When replacing \( f(x) \) with \( f(x-1) \), you're effectively shifting the graph horizontally. Specifically, \( f(x-1) \) shifts the graph of \( f(x) = \sqrt[3]{x} \) to the **right** by 1 unit.
**Answer:** The graph shifts right.
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Simplify this solution Bonus Knowledge
When \( f(x) \) is replaced by \( f(x-1) \), the graph of \( f(x) = \sqrt[3]{x} \) shifts to the right by 1 unit. This transformation occurs because every x-value of the original function is now reached at one unit greater on the x-axis, effectively moving the graph right. Now, if you think about it, visualizing such transformations can make it much easier to grasp the concept! Just remember, when you subtract from \( x \), it moves in the positive direction, the same way a clock hand moves as it ticks forward. It's almost like a dance move for the graph!
