heabcireddderPh heabcireddderPh
  • 21-11-2016
  • Mathematics
contestada

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 ...?

Respuesta :

alsteva alsteva
  • 22-11-2016
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,+∞)

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

[tex]y=\sqrt{4-x^2}[/tex]
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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