Question
Given the function \( f(x)=\sqrt[3]{x} \), what is the new function when \( f(x) \) is shifted 7 units to the right? Option \#1: \( f(x-7)=\sqrt[3]{x-7} \) Option \#2: \( f(x+7)=\sqrt[3]{x+7} \) Option \#3: \( f(x)+7=\sqrt[3]{x}+7 \) Option \#4: \( f(x)+7=\sqrt[3]{x}-7 \) (1 point) The best answer is Option \#
Ask by Watkins Salinas. in the United States
Jan 23,2025
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Answer
The best answer is Option #1: \( f(x-7) = \sqrt[3]{x-7} \).
Solution
The best answer is **Option #1**.
**Option #1:** \( f(x-7) = \sqrt[3]{x-7} \)
Shifting a function 7 units to the right involves replacing \( x \) with \( x - 7 \) in the function. Therefore, the correct shifted function is \( \sqrt[3]{x-7} \).
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Simplify this solution Bonus Knowledge
The function \( f(x)=\sqrt[3]{x} \) when shifted 7 units to the right is represented by the equation \( f(x-7) \). This means you're replacing \( x \) with \( x - 7 \), moving every point of the function to the right on the graph. So the correct choice is Option \#1: \( f(x-7)=\sqrt[3]{x-7} \). When you shift functions, remember that horizontal movements mean you manipulate \( x \) directly. So, with right shifts, you subtract from \( x \), while left shifts would add. It's like telling the graph, "hey, move over to the party at \( x = 7 \)!"
