1. Consider the function y = f(x) given by the following definition, where a and 3 are constants. (x+4)², if - 4 ≤ x < -

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1 Consider The Function Y F X Given By The Following Definition Where A And 3 Are Constants X 4 If 4 X 1 (43.14 KiB) Viewed 42 times

1. Consider the function y = f(x) given by the following definition, where a and 3 are constants. (x+4)², if - 4 ≤ x < -1; f(x) = a+2x, if - 1 ≤ x ≤ 1; B+4-x, if 1 < x≤ 4. (a) What is the domain of this function? (b) For a = 0 and 3 = 0, sketch the graph of y = f(x). You may tabulate the values o: f(x) for a few different choices of r in order to draw this graph, or use your knowledge of what the graphs of the individual expressions (linear functions, quadratic functions) look like. (c) For a = 0 and 3 = 0, what is the range of this function? (d) For a = 0 and 3 = 0: i. Find the one-sided limits lim f(x) and lim f(x). x→-1+ ii. Find f(-1). iii. Is the function f continuous at x = -1? Explain why or why not. (e) For what values of a and 3 is f continuous over its domain? Justify your answer. -[-+*