c1-t1t-a - NAME Brief Answers TEST1T/MAC2311 Page 1 of 5...

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NAME: Brief Answers TEST1T/MAC2311 Page 1 of 5 Read Me First: Show all essential work very neatly. Use correct notation when presenting your computations and arguments. Write using complete sentences. Be careful. Remember this: "=" denotes "equals" , " " denotes "implies" , and " " denotes "is equivalent to". Do not "box" your answers. Communicate. Show me the magic on the page. 1. (10 pts.) On the coordinate system below sketch the graph of the function g defined below. Label very carefully. (x + 1) 2 , x -1 g(x) = 1 + x , x < -1 See c1-t1t-g.htm y x 2. (10 pts.) If f(x) = 2x 2 - 3x, find f(x + h) - f(x) , h and simplify as much as possible algebraically. Kindly observe that there are no limits of any sort being taken here. f(x + h) - f(x) [2(x+h) 2 -3(x+h)] - [2x 2 -3x] = h h = 4x - 3 + 2h for h 0 after the algebraic dust settles.
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TEST1T/MAC2311 Page 2 of 5 3. (5 pts.) Using complete sentences and appropriate notation, provide the precise mathematical definition of a function f // A function f is a rule that associates a unique output with each input. If the input is denoted by x, then the output is
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