Question
Which of the following is the equation of the new function that is shifted horizontally 6 units to the left from \( f(x)=(x-2)^{3} ? \) (1 point) \( h(x)=(x+4)^{3} \) \( h(x)=(x-4)^{3} \) \( h(x)=(x-6)^{3} \) \( h(x)=(x-10)^{3} \)
Ask by Lambert Mckenzie. in the United States
Jan 23,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( h(x) = (x + 4)^3 \)
Solution
To shift the function \( f(x) = (x - 2)^3 \) **6 units to the left**, you replace \( x \) with \( x + 6 \):
\[
h(x) = f(x + 6) = ( (x + 6) - 2 )^3 = (x + 4)^3
\]
So, the equation of the new function is:
\[
h(x) = (x + 4)^3
\]
**Answer:** \( h(x)=(x+4)^{3} \)
Reviewed and approved by the UpStudy tutoring team
Like
error msg
Explain 
Simplify this solution Extra Insights
To shift a function horizontally to the left, you need to add to the x-value inside the function. Since your original function is \( f(x) = (x - 2)^{3} \), shifting it 6 units to the left means you will add 6 to the x-term. This gives us \( f(x + 6) = (x + 6 - 2)^{3} = (x + 4)^{3} \). So, the equation of the new function is \( h(x) = (x + 4)^{3} \). Just to clarify, many learners mistakenly just adjust the constants without considering the shift's direction. It's crucial to remember that moving left adds to the x-value, while moving right subtracts!
