I've been looking around on the internet, but I can't make much sense of the questions I have with the definitions for function that I'm getting, and I have answers but I'm not sure how correct they are.
I'm looking at the graph of a function.
1. What is the maximum number of times that the graph can intersect the y-axis.
I'm thinking that a function could only cross the y-axis once, because for the input 0 a function can only have 1 output.
2. Can the graph intersect the x-axis an infinite number of times?
My question is can a function be of an infinite degree? Does this scenario make sense?
3. If the function is a polynomial, how can you predict the number of times it might cross the x-axis?
The answer that I believe is right for this is that the polynomial function will have as many roots as the number of its degree, providing that all the roots are real numbers.
I feel like I know the first and third answers, but am unsure about the second and I think I could use a bit of conceptual help. Thanks to anyone who can help explain these scenarios to me!