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1 Reg. Pre-Calculus Multiple Choice. An epression is given. Evaluate it at the given value, (A) 0 (B) 9 9 (D) 0 (E). Simplif the epression. (A) (B) (D) (E) 0. Simplif the epression. (A) (B) (D) ( + ) (E). Simplif the epression. 9 9 (A) (B) (D) (E). Simplif the epression (A) (B) (D) 9 9. Simplif the epression. (A) (E) 9 9 (B) (D). Epress the function in the form f g. H A) f, g B) f, g C) f, g D) f, g st Semester Final Review. Epress the function in the form f gh. j (A) f, g, h (B) f, g, h f, g, h (D) f, g, h 9. Find the domain of g f, if f and. (A),, (B),,, (D), 0 0, g 0. Simplif the epression. 9 (A) (B) (D) (E) 9 9. Determine whether the given value is a solution of the equation., (A) es (B) no. Solve the equation. w w (A) (B) 9 (D) (E) 9 z. Solve the equation. z 9 (A) 9 (B) (D) (E) 0. Solve the equation. 0 (A) (B) (D) (E) 9. Solve the equation. (A) (B) (D) (E). Solve the equation. t t 0 (A) (B) (D) (E). Find all real solutions of the equation. 0 (A) none of these, (D) (B), (E),,

2 . Find all real solutions of the equation. (A), 0 (B) 0 (D) 0, (E) 9. Solve the linear inequalit. Epress the solution using interval notation. A), B), C), 0 D), E), 0. Solve the nonlinear inequalit. Epress the solution using interval notation. 0,,,, A) B) C), D), E),,. Solve the nonlinear inequalit. Epress the solution using interval notation., 9,,, A) B) C),, D),, E),,. Solve the inequalit. Epress the solution using interval notation. 0 A), B), C), D), E),. Solve the inequalit. Epress the solution using interval notation. 9 A) [, ) B) [, ) C) [, ) D) [, ) E) [, ). Solve the inequalit. Epress the answer using interval notation. 9 A) B) [, ] C), D),, E),,. A set of real numbers is graphed) Find an inequalit involving an absolute value that describes the set. A) B) C) D) E). Solve the nonlinear inequalit. Epress the solution using interval notation and graph the solution set. A), 0, B),, 0 C),, D) 0,,. Evaluate the function f at f(). A) f() = B) f() = C) f() = D) f() = E) f() = 0. Evaluate the function f at f (). A) f() =. B) f() =. C) f() =. D) f() =. E) f() = 9. Find the domain of the following function: 9 f A) (-, ) B) [0, ) C) (0, ) D) [, ) E) (-, ] 0. What is the domain and range of the function that is graphed below? (A) Domain: (, ), Range: [, ] (B) Domain: (-, ), Range: [, ] Domain: [, ], Range: [, ] (D) Domain: [, ], Range: (-, ) (E) Domain: [, ], Range: [, ]. What is the average rate of change of the function f between = 0 and =? A) B) C) D) E). What is the average rate of change of the function f between = 0 and =? A) B) C) 0 D) E). The graph of the function is sketched as follows: Determine the interval on which the function is increasing. A) (, ) B) (, ) C) (, ) D) (, ) E) (, ). How man units must we shift the graph of f to obtain the graph of f? A) left B) left C) right D) right E) left. The graph of a function is given as follows: - - -

3 Determine the average rate of change for the function between the indicated values of the variable. A) B) C) D). The graph of a function is sketched as follows: 0 Determine the average rate of change of the function between the indicated values. A) B) C) - D) E) -. The table shows the number of CD plaers sold in a small electronics store in the ears as follows: Year CD plaers sold What was the average rate of change of sales between 99 and 999? (A) 0 CD plaers/ear (B) 9 CD plaers/ear 0 CD plaers/ear (D) CD plaers/ear (E). CD plaers/ear. Suppose the graph of f is given. Describe how the graph of the function can be obtained from the graph of f. f (A) Shift the graph of f to the right units, stretch verticall b a factor of, and then shift downward units. (B) Shift the graph of f to the left units, stretch verticall b a factor of, and then shift downward units. Shift the graph of f to the right units, stretch verticall b a factor of, and then shift downward units. (D) Shift the graph of f to the left units, stretch verticall b a factor of, and then shift upward units. (E) Shift the graph of f to the left units, stretch verticall b a factor of, and then shift downward units. Short Answer 9. Perform the addition and simplif. 0. Perform the subtraction and simplif. 0. Find the length in the figure, if the shaded area is 9 in.. Perform the multiplication and simplif. 0. Determine whether the given value is a solution of the equation. 0 (A) = (B) =. Solve the equation. t0 t. Solve the equation b factoring. 0. Solve the equation b completing the square. Find all real solutions of the equation... Simplif ab 0t 9. Simplif 0s

4 0. Simplif:. Simplif: Multipl: 0. Multipl: 9. Factor: 0m m 0m 9. Factor:. Factor: 0. Factor:. Factor: 9. Multipl: 0. Simplif each radical and combine if possible:. Simplif each radical and combine if possible: 0 0. Simplif each radical and combine if possible:. Rationalize and simplif: 0. Rationalize and simplif:. Simplif:. Simplif:. Simplif: 9. If f, determine the graph of w? 9. Find the domain of the function. g 0. Sketch the graph of the piecewise defined function. if f if if. Sketch the graph of the piecewise defined function. if f if. A man is running around a circular track 00 m in circumference. An observer uses a stopwatch to record the runner's time at the end of each lap, obtaining the data in the table. Time (s) Distance (m) (a) What was the man's average speed (rate) between s and s? Please round our answer to the nearest hundredth. (b) What was the man's average speed (rate) between 0 s and 9 s? Please round our answer to the nearest hundredth. For the following, graph, determine the domain and range, and determine where the graph is increasing.. f. f. f.. f 9. f f. f 0. Determine where the function is increasing.. A function is given. Determine the average rate of change of the function between the values of the variable. g ; 0, h. Evaluate the following piecewise defined function at f, f, and f. f if if. Find the domain of the function. h

5 . The graph of g is given. Sketch the graph of the g function.. In a certain countr, income ta T is assessed according to the following function of income. 0 if 0 0, 000 T 0. if 0, 000 0, 000, if 0, 000 (A) Find T(,000). (B) Find T(,000). Find T(0,000).. Assume f is a one-to-one function. If f, find f.. Use f and g to evaluate f g.. Find the inverse function of f Find the inverse function of f. 90. Use the given graphs of f and g to evaluate the epression. (A) g f 9. Use f and g (B) g g to evaluate the epression. (A) f f (B) g g 9. Determine the equation of the piece-wise function. 9. Graph the following function:, f,, 9. Identif the value of sin - (.) (in degrees) 9. =, find ref 9. =, find ref 9. =, ref =? 9. Convert 0 into radians 99. Convert into radians 00. Convert into degrees 0. Convert into degrees 9 0. sin and terminates in Quadrant III, tan =? 0. sec and terminates in Quadrant IV, find csc 0. cos and terminates in Quadrant I, find cot 0. If the terminal side of passes through (, ), find tan. 0. If tan in Quadrant III, find csc 0. Which functions are positive in Quadrant I? 0. Which trigonometric functions are positive in Quadrant II? 09. Which trigonometric functions are positive in Quadrant IV? 0. csc is positive in Quadrants? Find:. tan. sec. sin. cos. cos 9. cos sin π. csc 0. cos sin. sec. cos sin. cos. sec csc

6 . Graph tan. Graph cos 0. Graph cos0. Graph sin 0. What is the amplitude of the following graph What is the horizontal shift if the graph is a sine curve? A cosine curve? Give the equation of the following curve Identif the period of cos 0. What transformation were performed on cos. Identif the equation of a sinusoid whose period is 0, whose vertical shift is, whose amplitude is, and whose horizontal shift for sin is 00.. Identif the equation of a sinusoid whose period is 0, whose vertical shift is, whose amplitude is, and whose horizontal shift for sin is.. Identif the range of cos sec 0. Identif the period of. Identif the vertical shift of cos. Identif the horizontal shift of 9sin 00 sin cos. Simplif tan 9. Show that csc sin cot cos csc 0. Prove cot csc cos. Simplif cos sin tan. Simplif cos csc cot cos cot sin. Simplif cos. Simplif cos sin tan. sin. sec9. Given with sin A with A and sin B with B, use identities to find eact values for a. cos A b. tanb c. sin A B d. cos A B. Determine a positive and negative coterminal angle to.

7 Answer Section ) A ) B ) B ) A ) C ) C ) B ) A 9) A 0) D ) A ) D ) E ) A ) E ) C ) D ) E 9) B 0) D ) C 9) 0) ) in. ) ) = is not a solution; = is a solution ) t ), ), ), ) a b t 9) s 0) ).... ) 0 ) m 0m m ) ) 9 ) ) ) 9) 0 0) 0 ) ) ) 0 ) ) ) E ) D ) D ) A ) B ) C ) E ) 9 ) ) 9) (-, ] 0) ) ) A) 00 ) ) B) ) A 0) C ) C ) A ) D ) B ) D D: (-, ) R: [-, ) Inc: (0, ) ) C ) D ) E

8 ) - ) ) D: (-, ) (, ) R: (-, 0) (0, ) Inc: none D: (-, ] R: (-, 0] Inc: (-, ) D: (-, ) R: (-, -] Inc: (-, ) 0) (-, ) ) h ) f, f, f 0 ), ) ) ) D: (-, ) R: (-, ) Inc: (-, ) D: (-, ) (, ) R:(, ) Inc: (-, ) ) (A) 0 (B) ) ) 9 ) f 9) f 90) A) B) 9) A) 9 B) 9) 0 f 0 9) D: (-, ) R: (-, ) Inc: (-, )

9 9) 0º 9) º 9) º 9) º 9) 99) 00).º 0) 0º ) 0) 0) 0) 0) 0) 0) All 0) sin, csc 09) cos, sec 0) I, II ) ) ) ) ) ) ) ) ) 9) 0) ) 0 ) ) ) ) ) º for sin; 0º for cos 9) cos or sin 0) 0º ) cos A: ; B: 0º; C: ; D: ) sin(( 00 )) ) sin(( )) ) [, ] ) º ) up ) 00º right ) cot 9) cos cot 0) csc cot ) sec ) sin ) csc ) sin ) ) ) a. 9 b. c. d. ) 9,