y 2 =8+2 x − x 2 ; x 2 − 2 x +1+ y 2 =9; ( x − 1) 2 +( y − 0) 2 =3 2 . The last is the equation of a circle with center (1 , 0) and radius 3. But y = 0, so the graph of f is the upper half of that circle, and it is shown in Fig. 1.MP.10. C01S0M.031: Given: f ( x )=2 − x − 1. The graph of y =2 x is an increasing exponential function, so the graph of y =2 − x is a decreasing exponential function, approaching 0 as x approaches + ∞ . So the graph of f approaches − 1as x approaches + ∞ . Moreover, f (0) = 0. Therefore the graph of f is the one shown in Fig. 1.MP.7. C01S0M.032: The graph of f ( x ) = log 10 ( x +1) is obtained from the graph of g ( x ) = log 10 x by translation one unit to the left; note also that f (0) = 0. Therefore the graph of f is the one shown in Fig. 1.MP.2. C01S0M.033: The graph of y = 3sin x oscillates between its minimum value − 3 and its maximum value 3, so the graph of f ( x )=1+3sin x oscillates between − 2 and 4. This graph is shown in Fig. 1.MP.8.
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This note was uploaded on 09/14/2011 for the course MATH 101 taught by Professor Cheng during the Spring '11 term at Ecole Hôtelière de Lausanne.