Thus, the xaxis is a horizontal asymptote The equation d d x e x = e x {\displaystyle {\tfrac {d}{dx}}e^{x}=e^{x}} means that the slope of the tangent to the graph at each point is equal to its y coordinate at that pointGraph of quadratic functions in vertex form g (x) = a (x h) 2 k A quadratic function in vertex form g (x) = a (x h) 2 k is the basic quadratic function f (x) = x 2 that has been transformed 1) From x 2 to (x h) 2 shift h units right if h is positive or h units left if h is negativeF0(x) = lim h!0 f(x h) f(x) h If the limit exists, f is said to be di erentiable at x, otherwise f is nondi erentiable at x If y= f(x) is a function of x, then we also use the notation dy dx to represent the derivative of f The notation is read "D yD x" Do not read it as "D yover D x", as the di erentials dy, dxare not numbers
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