algebraic function help

[merikukri]

Find an algebraic function with a domain of [-6, 5) and a range of (-infinity, 5] Graph Function

Please Help..

 

[stapel]

This exercise asks you to use what you know to invent something new. There is no one "right" answer.

What sorts of functions have restricted domains? Why are the domains restricted? What sorts of things give you "hard" edges (like "x > -6") and "soft" edges (like "x < 5")?

What sorts of functions have graphs that go down forever? What sorts of functions have ceilings that they don't surpass?

What are your thoughts?

Eliz.

 

[merikukri]

This exercise asks you to use what you know to invent something new. There is no one "right" answer.

What sorts of functions have restricted domains? Why are the domains restricted? What sorts of things give you "hard" edges (like "x > -6") and "soft" edges (like "x < 5")?

What sorts of functions have graphs that go down forever? What sorts of functions have ceilings that they don't surpass?

What are your thoughts?

Eliz.

I am somewhat getting the idea, but I am lost @ how I figure that out which satisfies the question...
thanks for ur help

 

[pka]

Think about \(\displaystyle \sqrt {6 + x}\) and about \(\displaystyle \sqrt {x - 5}\).

How would you combine these?
Would a fraction give an infinite range \(\displaystyle ( - \infty ,5]\).?

You may have to add a constant.

You can use a graphing utility to experiment.