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Which graph represents the function f(x)=|x-2|+1?

User Thomas Rbt
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1 Answer

5 votes

Answer:

Explanation:

The graph of the function f(x) = |x-2|+1 can be obtained by breaking the expression into two parts based on the definition of absolute value. When x is greater than or equal to 2, the expression evaluates to (x-2)+1 = x-1. When x is less than 2, the expression evaluates to -(x-2)+1 = 3-x.

Thus, we can write the function as:

f(x) = {x-1, x >= 2

{3-x, x < 2

The graph of the function f(x) looks like:

|

4 - | /\

| / \

3 - | / \

|/ \

2 - +--------\-------

0 1 2 3 4

Note that the graph has a corner point at (2, 1) where the two parts of the function meet. On the left side of the graph, the function is decreasing linearly from (2, 1) to (0, 3), while on the right side, the function is increasing linearly from (2, 1) to (4, 3).

User Finlay
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