Write as a Function of x y=|4-x|

Problem

y=|4−x|

Solution

1. Identify the definition of the absolute value function, which states that |u|=u if u≥0 and |u|=−u if u<0

2. Determine the critical point by setting the expression inside the absolute value to zero: 4 - x = 0,w*h*i*c*h*g*i*v*e*s() = 4$.

3. Analyze the first case where 4−x≥0 This inequality simplifies to x≤4 In this interval, the function is y=4−x

4. Analyze the second case where 4−x<0 This inequality simplifies to x>4 In this interval, the function is y=−(4−x) which simplifies to y=x−4

5. Combine these cases into a piecewise-defined function.

Final Answer

ƒ(x)={[4−x,if *x≤4],[x−4,if *x>4])

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