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What are the horizontal and vertical shifts for the absolute value function below?

[tex]\[ f(x) = |x - 5| + 1 \][/tex]

Sagot :

GinnyAnsweridn
Let's examine the given function to identify the horizontal and vertical shifts:

[tex]\[ f(x) = |x - 51| + 1 \][/tex]

1. Horizontal Shift:
- The term inside the absolute value, [tex]\( x - 51 \)[/tex], represents a horizontal shift.
- To determine the horizontal shift, we look for a value that transforms [tex]\( x \)[/tex] to zero. In this case, [tex]\( x - 51 \)[/tex] shifts [tex]\( x \)[/tex] to the right by 51 units.
- Therefore, the horizontal shift is 51 units to the right.

2. Vertical Shift:
- The term outside the absolute value, [tex]\( + 1 \)[/tex], represents a vertical shift.
- This term shifts the entire function upward by 1 unit since it is added to the absolute value function.
- Therefore, the vertical shift is 1 unit upward.

Thus, the horizontal shift is 51 units to the right, and the vertical shift is 1 unit upward.
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