MAT135H1 Lecture Notes - Lecture 1: Asymptote, Inverse Trigonometric Functions, Exponential Function
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MAT135H1 Full Course Notes
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Translations: c is a positive number -> graph y= f(x) + c is just y=f(x) shifted upwards a distance of c units. If g(x) = f(x-c) where c>0 then value of g at x is the same as the value of f at x c. thus f(x-c) is f(x) shifted c units to the right. Combination of functions f and g can be combined to form new functions: f + g, f g, and f/g. The sum and difference functions are defined by (f + g)(x) = f(x) + f(g) (f g)(x) = f(x) g(x) If dom of f is a and dom of g is b, then dom of f+g is a b. Domain of fg is a b but we cant divide by 0, so the domain of f/g is {xe a b | g(x) (f/g)(x) = [f(x)/g(x)] 1. 4 exponential functions f(x)=bx is a positive constant. If x=n, a positive integer then bn = (b)(b) (b)
