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What are the domain and range of y=-5/6(x+2)^2-8?


PLEASE HELP WILL MARK BRAINIST AND GIVE OUT FREE MORE POINTS IF YOU ARE CORRECT I DO CHECK IT PLEASE AND THANK YOU !!

What are the domain and range of y56x228 PLEASE HELP WILL MARK BRAINIST AND GIVE OUT FREE MORE POINTS IF YOU ARE CORRECT I DO CHECK IT PLEASE AND THANK YOU class=

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Answer:

Domain: allrealnumbers

Range: f(x) <= -8

Step-by-step explanation:

This equation shows that this shape is a parabola that is opening downwards (because of the negative in the -5/6)

This means it has a highest point. The x+2 means the curve is shifted/slid/tranlated to the right 2 units and the -8 at the end shows that it is slid/shifted/translated down 8 units. So the curve only exists starting from -8 and going down. That is the range f(x) <= -8

All upward and downward opening parabolas have a domain of all real numbers.

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Let's see

[tex]\\ \rm\rightarrowtail y=\dfrac{-5}{6}(x+2)^2-8[/tex]

[tex]\\ \rm\rightarrowtail x\in R[/tex]

  • As x lies on numerator for all real numbers its true and never gets undefined

Domain is R

Now

[tex]\\ \rm\rightarrowtail y=\dfrac{-5(x+2)^2}{6}-8[/tex]

Vertex form of parabola:-

  • y=a(x-h)²+k

On comparing with this

  • Vertex=(h,k)=(-2,-8)

Hence

Range :-

  • y≤-8
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