Question
Let the function be \( f(x)=x^{3} \). Which of the following functions represent the transformation of \( f(x) \) shifted horizontally to the left 4 units? Option \#1: \( g(x)=(x-4)^{3} \) Option \#2: \( g(x)=(x+4)^{3} \) Option \#3: \( g(x)=(x)^{3}-4 \) (1 point) The best answer is Option \# \( \square \).
Ask by Weaver Conner. in the United States
Jan 23,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The best answer is Option #2.
Solution
The best answer is Option #2.
**Explanation:**
- To shift the function \( f(x) = x^3 \) **horizontally to the left by 4 units**, you replace \( x \) with \( x + 4 \).
- Therefore, the transformed function is \( g(x) = (x + 4)^3 \), which corresponds to **Option #2**.
Answer: The best answer is Option #2.
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Simplify this solution Bonus Knowledge
When you're looking to shift a function horizontally, the transformation is done inside the function's argument. To shift \( f(x) = x^3 \) to the left by 4 units, you need to substitute \( x \) with \( x + 4 \). So, the correct form would be \( g(x) = (x + 4)^3 \). Therefore, the best answer is Option \#2.
