The function y=x is a straight line. The range is all real numbers.
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If x = sin θ and y = cos θ then: sin² θ + cos² θ = 1 → x² + y² = 1 → x² = 1 - y²
Both. If you look at it like this: y=41-x you say x is independent and y is dependent of x (i.e. y is a function of x) For x=41-y you say y is independent and x is dependent of y (i.e. x is a function of y)
y = 4(2x) is an exponential function. Domain: (-∞, ∞) Range: (0, ∞) Horizontal asymptote: x-axis or y = 0 The graph cuts the y-axis at (0, 4)
Because the derivative of e^x is e^x (the original function back again). This is the only function that has this behavior.