Without looking up the exact definition, a function of variable x: y = f(x), will have only one value for each value of x. (So it would not cross over itself, or another way, given any value of x there will only be one corresponding y value). So a circle is not a function, because there are 2 possible y values for each x value in the range of the circle.
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No, a circle graph is never a function.
sine graph will be formed at origine of graph and cosine graph is find on y-axise
A line. The derivative of a function is its slope. If the slope is a constant then the graph is a line.
A derivative graph tracks the slope of a function.
If the graph is a function, no line perpendicular to the X-axis can intersect the graph at more than one point.