Math 260 Test#1 Practice Test
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MATH 260 TEST#1 PRACTICE TEST
1. Solve the equation: 3x 1 4 1 1 (a) 3 x x 3 (b) (c) 6 3 x 2 x 2 x 2 4 x 2x 8 0 (d) x 4 8x 2 9 0
2. Solve the nonlinear inequality. Express the solution using interval notation x 2 (a) 4 (b) x 2 x 12 0 3x 5
3. Solve the equation a) 3x 5 4 b) 3 x 2 4 25
4. Solve the inequality and write the solution in interval notation. (a) x 5 9 (b) 2x 5 4
5. Write the expression in the form a bi 5 121 6 3i (a) (b) 1 25 2 7i
2 4 x 2x 1 6. Simplify the expression 5 8 x 2x 1
7. Find the domain of the function 2x 1 x (a) f (x) (b) 2x 5 x 2 4
8. Determine whether f is even, odd, or neither. Explain. (a) f x 3x 4 2x 2 3 (b) f x 5x3 3x 2 3x 2 9. Sketch the graph of the piecewise defined function x 3 if x 2 2 x if 2 x 1 x 4 if x 1
10. Use f (x) 2x 2 5x 1and g(x) 3x 2 to evaluate the expressions. a) ( f ° g)(x) b) (g ° f )(x) c) g( f (1)) d) f g5 e) f gx
11. If f x x 15 and gx x 2 2x , find the following functions and their domains a) f ° gx b) g ° f x
12. Sketch the graph of the function, not by plotting points, but by starting with the graph of a standard function and applying transformations. 1 a) y x 3 2 3 b) y 2 x 2
13. Identify the graph of the equation and determine whether the equation defines y as a function of x . Why or why not? a) x 2 y 2 4 b) y x 2
14. Find an equation of a line through P(3,2), Q(2,4) . Write the equation in slope intercept form and standard form.
15. Find the domain of the function: x 4 a) f x x 2 x 6 b) f x 7 3x 16. A certain country taxes the first $20,000 of an individual’s income at a rate of 15%, and all income over $20,000 is taxed at 20%. Find a piecewise-defined function T that specifies the total tax on an income of x dollars.
17. For children between ages 6 and 10, height y (in inches) is frequently a linear function of age t (in years). The height of a certain child is 48 inches at age 6 and 50.5 inches at age 7. a) Express y as a function of t b) Predict the height of the child at age 10.
18. Graph the piecewise defined function: x if x 0 a) f x x 1 if x 0 4 if x 2 2 b) f x x if 2 x 2 x 6 if x 2 19. Westside Energy charges its electric customers a base rate of $6.00 per month, plus 10cents per kilowatt-hour(kWh) for the first 300 kWh used and 6Centes per kWh for all usage over 300kWh.Suppose a customer uses x hWh of electricity in one month. Express the monthly cost E as a piecewise defined function of x.
20. The graph of a function h is given. Find: a) h(-2), h(0), h(2) and h(3) b) Find the domain and range of h c) Find the values of x for which h(x)=3 d) Find the values of x for which h( x) 3 e) Find the net change in h between x=-3 and x=3 21. Use the graph to estimate all the local minimum and maximum, the intervals on which the function is increasing and decreasing
22. Given the function, find the average rate of change between the given values of the variable. f x x3 4x 2 , x 0, x 10 23. The table gives the population in a small coastal community for the period 1997- 2006. Figures shown are for January 1 in each year. a) What was the average rate of change of population between 1998 and 2001? b) What was the average rate of change of population between 2002 and 2004? c) For what period of time was the population increasing? Decreasing? 24. Find the inverse function: x 2 a) f x x 2 b) f x 3x 3 8 c) f( x) =4 - x2 ; 0＃ x 2
25. Mr. Jonh charges a base price of $18 for a large pizza plus $1.75 for each addition topping. a) Find a function f that models the price of a pizza with n toppings b) Find the inverse of the function f . What does f -1 represent
26. Express the statement as an equation. Use the given info to find the constant of proportionality: a) A varies inversely as r. If r=3 then A=7 b) S is proportional to the product of p and q. If p=4 and 1=5 then S=180
27. Find the center and radius for the circle and sketch the graph x 2 y 2 4x 6y 12 0
28. Find an equation for the circle with Center(-1,-4); radius 8