No.The equation x/(x^2 + 1) does not have a vertical asymptote.
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No, this is not a function. The graph would have a vertical line at x=-14. Since there are more than one y value for every given x value, the equation does not represent a function. The slope of the equation also does not exist.
If for every point on the horizontal axis, the graph has one and only one point corresponding to the vertical axis; then it represents a function. Functions can not have discontinuities along the horizontal axis. Functions must return unambiguous deterministic results.
That's true. If a function is continuous, it's (Riemman) integrable, but the converse is not true.
No. A function is a "graph" the survives the "vertical line test". Namely, it is for every x in its domain, there can be one and only one f(x) in its co-domain. An ellipse clearly fails it at everywhere except it's two vertex. But an ellipse can be thought as two separate functions. A standard ellipse relation, x^2 / a + (y)^2 / b = 1, can be thought as two separate real functions of y1 and y2. where y1 = -y2 exactly.
For every vertical foot of pipe, take that and multiply it by .434.This equation will get within 1/2 -1/4 psi.