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For which values does the cosecent functions have x intercepts?
The cosecant function, being defined as 1÷sin(x), has no x intercepts. It has y intercepts at ±∞. (infinity and -infinity)
What is the difference of x intercept and y intercept?
The y-intercept is the value of the function when 'x' is zero. That is, it's the point at which the graph of the function intercepts (crosses) the y-axis. The x-intercept is the value of 'x' that makes the value of the function zero. That is, it's the point at which 'y' is zero, and the graph of the function intercepts the x-axis.
How many y intercepts does a sine function have?
One intercept of the y-axis and infinitely many of the x-axis.
Why the graph of a polynomial function with real coefficients must have a y-intercept but may have no x-intercept?
For a polynomial of the form y = p(x) (i.e., some polynomial function of x), having a y-intercept simply means that the polynomial is defined for x = 0 - and a polynomial is defined for any value of "x". As for the x-intercept: from left to right, a polynomial of even degree may come down, not quite reach zero, and then go back up again. A simple example is y = x2 + 1. Why is the situation for "x" and for "y" different? Well, the original equation is a polynomial in "x"; but if you solve for "x", you don't get a polynomial in "y".
What if you cant do find the x intercepts?
Then there is no x-intercept. No big deal. Lots of functions do not have x- intercepts. For example, y = x2 + 1 or y = 2x
