Question

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

Answer 1

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

Answer 2

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.