Question

Find the domain and range of the graphs:

y=2^x
y=x^2-4
y=x^2+4x+3
y=sqrt(x-2)
y=sqrt(4-x^2)
y=|x+3|-2 ...?

Answer 1

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=√(x-2)`
Domain:
x-2≥0⇒x≥2
x∈[2,+∞)
Range: y∈[0,+∞)


`y=√(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,+∞)