quiz1_correc-1

quiz1_correc-1 - CORRECTION AND COMMENTS Quizz 1, Sept 4...

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Unformatted text preview: CORRECTION AND COMMENTS Quizz 1, Sept 4 Math 118: 39439 Fall 2008 Name (in capitals): Present answers clearly and with reasonable detail in this page. If needed, use the back of this sheet for scratch. You have 25 minutes for this 5 points quiz. Good work. Consider the functions f (x) = and g(x) = x + 1. PROBLEM x-2 x-1 (a) (1 pts) Indicate the domain of f (x). Since x - 1 is not allowed to be zero, the domain of f (x) is all real numbers except number 1. 1 (b) (1 pts) Find the composition f (g(x)). f (g(x)) = f (x + 1) = (x + 1) - 2 x + (1 - 2) x-1 = = . (x + 1) - 1 x + (1 - 1) x PROBLEM Consider a supply price function given by S(x) = x2 - 3x - 10, also, consider a demand price function given by D(x) = 6 - 3x, where x stands for the number of units of a certain commodity. (a) (2 pts) Name pe the equilibrium price and xe the equilibrium number of units. Find xe and pe . Equilibrium price occurs when demand equals supply. Search for x s.t.: S(x) = D(x) x2 - 3x - 10 = 6 - 3x x2 - 3x - 10 - 6 + 3x = 0 x2 - 16 = 0 (x - 4)(x + 4) = 0 1 Comments: etc. with symbols this can be written as x = 1,R\{1}, (-, 1)(1, +), {x R; x = 1}, i x = -4 or x = 4. Since x refers to number of units it should be positive. Therefore xe = 4. To nd pe , plug in the xe in demand or supply. D(4) = 6 - (3)(4) = -6. Since we shouldn't allow negative prices either, this problem has no solution. Mathematically, by solving D(x) = S(x) we will obtain two solutions xe = 4 and pe = -6 or xe = -4 and pe = 18, which correspond to the two points of intersection of the graphs of the functions S(x) and D(x). (b) (1 pts) Sketch of the graph of D(x) indicating its x-intercept and y intercept. The y -intercept is (0, 6) because D(0) = 6 - (3)(0) = 6; the x-intercept is (2, 0) because 0 = 6 - 3x i x = 2. The graph is a line through those points. End. ...
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quiz1_correc-1 - CORRECTION AND COMMENTS Quizz 1, Sept 4...

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