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f(x)={[-(1)/(2)x-4," |f "x < -1],[(x-2)^(2)," if "-1 <= x < 3],[|x-5|-3," if "x >= 3]:}

f(x)={−12x−4 |f x<−1(x−2)2 if −1≤x<3∣x−5∣−3 if x≥3 f(x)=\left\{\begin{array}{cl}-\frac{1}{2} x-4 & \text { |f } x<-1 \\ (x-2)^{2} & \text { if }-1 \leq x<3 \\ |x-5|-3 & \text { if } x \geq 3\end{array}\right.

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Q. f(x)={−12x−4 |f x<−1(x−2)2 if −1≤x<3∣x−5∣−3 if x≥3 f(x)=\left\{\begin{array}{cl}-\frac{1}{2} x-4 & \text { |f } x<-1 \\ (x-2)^{2} & \text { if }-1 \leq x<3 \\ |x-5|-3 & \text { if } x \geq 3\end{array}\right.
  1. Identify Transformation: Identify the transformation needed for f(x)f(x) to become g(x)g(x). Translation 55 units up means adding 55 to the function's value.
  2. Apply Transformation: Apply the transformation to the first part of f(x)f(x) for x<−1x < -1.g(x)=(−(12)x−4)+5g(x) = (-(\frac{1}{2})x - 4) + 5Simplify the expression.g(x)=−(12)x+1g(x) = -(\frac{1}{2})x + 1

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