To determine how function [tex]\( f_2 \)[/tex] compares to [tex]\( f_1 \)[/tex], we examine their definitions:
- [tex]\( f_1(x) = x \)[/tex]
- [tex]\( f_2(x) = x + 4 \)[/tex]
Let's analyze these step by step:
1. Understand the base function [tex]\( f_1 \)[/tex]:
- [tex]\( f_1(x) = x \)[/tex] is a linear function with a slope of 1 and a y-intercept of 0.
2. Analyze the transformation applied to [tex]\( f_1 \)[/tex] to get [tex]\( f_2 \)[/tex]:
- [tex]\( f_2(x) = x + 4 \)[/tex] takes every output of [tex]\( f_1(x) = x \)[/tex] and adds 4 to it.
This transformation represents a vertical shift of [tex]\( f_1 \)[/tex]. Specifically:
- Adding 4 to the function [tex]\( f_1(x) \)[/tex] shifts it vertically upwards by 4 units.
Conclusion:
- [tex]\( f_2 \)[/tex] is the function [tex]\( f_1 \)[/tex] moved 4 units up.
Thus, the correct answer is:
- Moved 4 units up.
