Question

Does a monomail function always, sometimes, or never pass through (0,0)? Explain your choice thoroughly.

Does a power function always, sometimes, or never pass through (0,0)? Explain your choice thoroughly.

Answer 1

See below.

First One: sometimes

Second one: yes if r>0 No if r < 0

Explanation:

Hmmmm! Very interesting question. We need 2 things.

• We need a monomial
• We need it to be a function

So y = x^2 is a function and passes through 0,0. Looking good.

y = x^3 is a function and it goes through 0,0 still looking good.

and y = x is both as well and it goes through 0,0. Are there any exceptions?

How about y = 4. It's a function. OH - OH. it does not go through 0,0

So the best choice is most of the time. I like most of the time better than sometimes, because there is only that one exception y = a.

y = a*(x^r). That's a power function. It is a monomial.

Be careful with this. If r>0 then all is good. 0,0 is a solution because x can = 0.

You get into trouble when r<0

y = a * 1/x^r Now when x = 0 the solution is undefined. So as long as r>0 then 0,0 is a solution and the answer is sometimes. Nasty!