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Verified Answer :

y=2^x
Domain: x∈R
Range: y∈(0,+∞)

y=x²-4
Domain: x∈R
Range:
y'=(x²-4)'=2x ⇒ x=0,y(0)=0²-4=-4
y∈(-4,+∞)

y=x²+4x+3
Domain: x∈R
Range: 
y'=(x²+4x+3)'=2x+4 ⇒ x=-2,y(-2)=(-2)²+4(-2)+3=4-8+3=-1
y∈(-1,+∞)

\(y=\sqrt{x-2}\)
Domain:
x-2≥0⇒x≥2
x∈[2,+∞)
Range: y∈[0,+∞)

\(y=\sqrt{4-x^2}\)
Domain: 
4-x²≥0⇒x²≤4⇒-2≤x≤2
x∈[-2,+2]
Range: x²≤4⇒y∈[0,2]

y=|x+3|-2
Domain: x∈R
Range: |x+3|≥0⇒y∈[-2,+∞)

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