1. An exploration into how to create and analyze a function from something that is not...

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1. An exploration into how to create and analyze a function from something that is not a function. (a) Identify and sketch the graph of the following equation, providing as much detail as possible (e.g., points of intersection, local maximum or minimum points, or asymp- totes). x-16y28x32y = 1. (b) A section of the graph in (a) is used to define a function, y = f(x), whose range is the interval Ry=[-1,3]. Determine the corresponding domain of f(x), D = [Xa,Xb] such that <6. Show all working. (c) Suppose we now wish to create a piecewise function, y = F(x), defined as follows. xD = [Ia, Ib], f(x), F(x) = x-4, x = (x1, 6]. i. Determine the following function values: F(-1)= ; F(0)= ; F(3) = ii. Determine the following left-hand and right-hand limits: lim F(x); lim F(x). iii. Does the limit of F(x) exist at x=x? Give reasons for your answer. iv. Is F(x) continuous at ? Give reasons for your answer. 1. An exploration into how to create and analyze a function from something that is not a function. (a) Identify and sketch the graph of the following equation, providing as much detail as possible (e.g., points of intersection, local maximum or minimum points, or asymp- totes). x-16y28x32y = 1. (b) A section of the graph in (a) is used to define a function, y = f(x), whose range is the interval Ry=[-1,3]. Determine the corresponding domain of f(x), D = [Xa,Xb] such that <6. Show all working. (c) Suppose we now wish to create a piecewise function, y = F(x), defined as follows. xD = [Ia, Ib], f(x), F(x) = x-4, x = (x1, 6]. i. Determine the following function values: F(-1)= ; F(0)= ; F(3) = ii. Determine the following left-hand and right-hand limits: lim F(x); lim F(x). iii. Does the limit of F(x) exist at x=x? Give reasons for your answer. iv. Is F(x) continuous at ? Give reasons for your answer.