SOLUTION: Hello, I would greatly appreciate your help on these questions. We have seen a parabola intersecting the x-axis twice and y-axis once. 1. Does any graph of any function inter

Question 329221: Hello,
I would greatly appreciate your help on these questions.
We have seen a parabola intersecting the x-axis twice and y-axis once.
1. Does any graph of any function intersect both the axes at least once? twice? or more?
2. How about a function that doesn't intersect any of the axes? Discuss with examples.
Thanks so much for your time!
Vanessa
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
We have seen a parabola intersecting the x-axis twice and y-axis once.
1. Does any graph of any function intersect both the axes at least once? twice? or more?
No. y = 2 is parallel to the x-axis, so there's no intersection of it. Only 1 intersection of the y-axis.
------------------------------
2. How about a function that doesn't intersect any of the axes?
eg, the circle (x-5)^2 + (y-5)^2 = r^2 doesn't intersect either asix, if r is less than 5.
A circle can be composed of 2 functions. Neither half will intersect the axes.
---------------
Discuss with examples.
I did.

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