Can someone check my answer? Thanks! :)

Select the graph and end behavior description of f(x) = 3 + x6.

Graph is a flattened parabola with vertex at 0, 3 and opens down. This is an even function. The end behavior of the graph will decrease to the right and to the left.

Question

Can someone check my answer? Thanks! :)

Select the graph and end behavior description of f(x) = 3 + x6.

Graph is a flattened parabola with vertex at 0, 3 and opens down. This is an even function. The end behavior of the graph will decrease to the right and to the left.

jim_thompson5910 · Answer

the leading term is x^6

it is positive, so this means that the graph must open upwards

anonymous · Answer

Oh!! Would the vertex be at 0, 3 or 0, -3?

jim_thompson5910 · Answer

well when x = 0, what is y?

jim_thompson5910 · Answer

to find out, plug it into the function and evaluate

anonymous · Answer

I'm not 100% sure how to do that. :( Could you teach me?

jim_thompson5910 · Answer

the function is f(x) = 3 + x^6

jim_thompson5910 · Answer

plug in x = 0 to get

f(x) = 3 + x^6

f(0) = 3 + (0)^6

f(0) = ???

anonymous · Answer

positive 3 
so the vertex would be 0, 3

jim_thompson5910 · Answer

good

jim_thompson5910 · Answer

(0,3) actually, but you got the idea

anonymous · Answer

thank you thank you! :)
Oh! (0,3)

jim_thompson5910 · Answer

you're welcome

and the end behavior would be seen if you graphed it or tried to visualize it in your mind