This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
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, xintercept, and yintercept 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 company’s revenue and cost functions respectively for sales of this good....
View
Full Document
 Spring '09
 crespo
 Calculus, Derivative, Slope, YIntercept, lim, Continuous function

Click to edit the document details