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Nitella [24]
2 years ago
11

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

Mathematics
2 answers:
Lesechka [4]2 years ago
6 0

Let's see

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

\\ \rm\rightarrowtail x\in R

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

Domain is R

Now

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

Vertex form of parabola:-

  • y=a(x-h)²+k

On comparing with this

  • Vertex=(h,k)=(-2,-8)

Hence

Range :-

  • y≤-8

marusya05 [52]2 years ago
4 0

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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