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Pre-Calculus: Chapter 1 Review No Calculators 1. As an employee in sales, you receive a monthly salary of $1800 plus a commission of 4% of your sales. Write an equation expressing the monthly wages y in terms of sales x. If you receive $3700 in wages for the month of January, what were your sales for that month? Name: ________________ 2. A rectangle of length x and width w has a perimeter of 60 meters. a) Draw a diagram b) Write the function for Area in terms of x. c) What is the domain of the function? 3. Determine the equation of the line that passes through the point (4, -5) and is perpendicular to 3 y x7. 5 4. Find the difference quotient and simplify your answer: f ( x) 5x 2 2 x 1 5. Determine algebraically if the function is even, 6. Use the algebraic tests to check for symmetry with respect to both axes and the origin. y 6 x3 odd, or neither. f ( x) 2 x x 3 2 f (3 h) f (3) ,h 0 h 7. Write an equation for the following function: 8. List the transformations in order and graph. f ( x) x 1 4 9. List the transformations in order and graph. 3 h( x ) 2 x 3 10. Graph the piecewise function x 2, x 2 h( x) x 2 1, 2 x 1 4 2 x, x 1 11. Describe the intervals on which the function is increasing, decreasing, or constant. 1 2x 5 12. Find f ( x) if f ( x) 7x 1 x 1 7 13. Find the average rate of change from x1 to x2 . f ( x) x 2 3x 5 x1 2 x2 5 15. Given f ( x) x 2 9 and g ( x) 9 x 2 a) Find the domain of f b) Find the domain of g c) Find f ( g( x)) 14. Find two pairs of functions f and g such that 3 f ( g ( x)) h( x) if h( x) (2 x 1)3 16. The weekly cost C of producing x units in a manufacturing process is given by C ( x) 60 x 750 . The number of units x produced in t hours is given by x(t ) 50t , 0 t 40 where t is the time in hours. a) Find the composition C x t b) Interpret the meaning of C x t in context of the problem. d) Find the domain of f ( g( x)) c) Find the weekly cost after 24 hours. d) Find the time when the weekly cost exceeds $15,000.