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Unformatted text preview: Worksheet # 1: Review 1. (MA 113 Exam 1, Problem 1, Spring 2007). Find the equation of the line that passes through (1 , 2) and is parallel to the line 4 x + 2 y = 11. Put your answer in y = mx + b form. 2. Find the slope, x-intercept, and y-intercept of the line 3 x- 2 y = 4. 3. Write the equation of the line through (2 , 1) and (- 1 , 3) in point slope form. 4. Write the equation of the line containing (0 , 1) and perpendicular to the line through (0 , 1) and (2 , 6). 5. The quadratic polynomial f ( x ) = x 2 + bx + c has roots at- 3 and 1. What are the values of b and c? 6. Let f ( x ) = Ax 2 + Bx + C . If f (1) = 3, f (- 1) = 7, and f (0) = 4 what are the values of A,B and C ? 7. Find the intersection of the lines y = 5 x + 10 and y =- 8 x- 3. Remember that an intersection is a point in the plane, hence an ordered pair. 8. Recall the definition of the absolute value function: | x | = x x - x x < . Sketch the graph of this function. Also, sketch the graphs of the functions | x + 4 | and | x | + 4. 9. A ball is thrown in the air from ground level. The height of the ball in meters at time t seconds is given by the function h ( t ) =- 4 . 9 t 2 + 30 t . At what time does the ball hit the ground? Units! 10. True or false? (a) For any function f , f ( s + t ) = f ( s ) + f ( t ). (b) If f ( s ) = f ( t ) then s = t . (c) A circle can be the graph of a function. (d) A function is a rule which assigns exactly one output f ( x ) to every input x. (e) If f ( x ) is increasing then f (- 52 . 55) f (1752 . 0001). Worksheet # 2: Functions and Inverse Functions; Logarithms 1. (MA 113 Exam I, Problem 2, Spring 2009). Consider the function f ( x ) = 4 x + 1 3 x- 2 . Determine the inverse function of f . 2. Let f ( x ) = x 3 + 1 and g ( x ) = x . Find ( f g )( x ) and ( g f )( x ) and specify their domains. 3. Suppose the graph of f ( x ) is given. Write an equation for the graph obtained by first shifting the graph of f ( x ) up 3 units and left by 2 units, and then compressing the resulting graph horizontally by a factor of 10. 4. Suppose the graph of g ( x ) is given by the equation g ( x ) = f (2 x- 5) + 7. In terms of standard transformations describe how to obtain g ( x ) from the graph of f ( x ). 5. Find the domain and range of the following functions. (a) f ( x ) = 15 (b) f ( x ) = x 2 + 2 x + 1 (c) f ( x ) = x 2- 2 x- 3 (d) f ( x ) = x | x | 6. Profit is the difference between total revenues and total costs. Suppose that Company W produces good Y. Let x denote the quantity of good Y sold. Suppose R ( x ) = 15 x and C ( x ) = 1 10 x 2 + x + 30 are the companys revenue and cost functions respectively for sales of this good....
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