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Compared to the parent function f (x) = x², how has the graph f (x) = (x+8)² been translated?
A It has been translated 8 units down.
B) It has been translated 8 units to the left.
It has been rotated -8 units.
It has been translated 8 units to the right.
It has been translated 8 units up.

Sagot :

GinnyAnsweridn
Let's analyze the function transformation step-by-step:

1. Understanding the Parent Function:
- The parent function given is [tex]\( f(x) = x^2 \)[/tex]. This is a parabola that opens upwards with its vertex at the origin, [tex]\((0,0)\)[/tex].

2. Transforming the Function:
- We are comparing it to the function [tex]\( g(x) = (x+8)^2 \)[/tex].

3. Horizontal Translations:
- Adding or subtracting a constant inside the parentheses (inside the argument of the function) affects the horizontal position of the graph.
- If we have [tex]\( f(x) = (x - h)^2 \)[/tex], the graph would shift [tex]\( h \)[/tex] units to the right if [tex]\( h \)[/tex] is positive.
- Conversely, if we have [tex]\( f(x) = (x + h)^2 \)[/tex], the graph shifts [tex]\( h \)[/tex] units to the left if [tex]\( h \)[/tex] is positive.

4. Identifying the Shift:
- In the function [tex]\( g(x) = (x+8)^2 \)[/tex], we see [tex]\( +8 \)[/tex] inside the parentheses.
- This indicates a horizontal translation to the left by 8 units.

Conclusion: The graph [tex]\( f (x) = (x+8)^2 \)[/tex] has been translated 8 units to the left compared to the parent function [tex]\( f(x) = x^2 \)[/tex].

Therefore, the correct answer is:

B) It has been translated 8 units to the left.
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