MSLC Math 1075 Final Exam Review. 1. Factor completely Solve the absolute value equation algebraically. g. 8x b. 4x 2 5x. f.

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1 MSLC Math 07 Final Exam Review Disclaimer: This should NOT be used as your only guide for what to study.. Factor completely. a. x y xy xy mn n 7x x x x 0xy x y e. xy y x y f. z z 7 g. mn m n h. c d i. m p j. v v k. x xy y z. Solve the absolute value equation algebraically. a. x x x 7 x. Solve the following inequalities algebraically. Give your answers in interval notation. x x a. 7 x x 7 x e. x f. 7 x g. x. Given set A [,] and set B (, ] a. A B A B determine:. Graph the solution sets to the following system of linear inequalities. a. xy xy x y

2 . Solve by factoring: a. x 0x x x 0 x x x x 7. Find the domain of each of the following functions. Give your answer in interval notation. a. g x x j x k x ( ) x 7 x. The minimum charge for a taxi ride is $.0, plus $0. per 0. mile. How many miles can you travel if you have at most $0. to spend on taxi fare?. Use the square root property to find the exact answer to each of the following. Make sure to completely simplify your answers. a. n m 0 0 x 0. Use completing the square to find the exact answer of the following. Make sure to completely simplify your answers. a. p 0 p 0 0 w w 7. Use the quadratic formula to find the exact answer of the following. Make sure to completely simplify your answers. a. a a b b. Simplify the following powers of i. a. i i i 0. Two airplanes leave the same airport at the same time. One airplane flies due south, while the other flies due west 0 mph faster than the first plane. After hour the airplanes are 0 miles apart. Find the speed of each airplane.

3 . Reduce the following rational expressions into lowest terms. m a. m m x xy y x y ax bx ay by xy c cd d w c 0b w. Perform the indicated operations and reduce the result into lowest terms. Assume that the variables are restricted to values that prevent division by 0. x x x x a. x x x x x x x 7 x x x. Use the given functions f x x, g x x, and h x a. f g h to find each of the following: x 7 f a g m e. f h f. f g g. gh 7 h. 7 i. g f x j. h f 7. Write an equation for each of the variation statements given: a. A varies directly as B cubed m varies directly as the square root of n and inversely as the square of p y varies jointly as x and the cube root of z and inversely as the square root of w. The distance required for an emergency stop for a car varies directly as the square of the speed of the car. A car travelling 0 miles per hour requires 0 feet to stop. a. What is the constant of variation? Write an equation relating the stopping distance to the speed of the car. How many feet will the car need to make an emergency stop if it is travelling at 70 miles per hour? How fast was the car travelling if it required. feet to make an emergency stop?. Perform the indicated operations. Make sure you completely simplify your answers. i i i a. i i i i

4 0. Solve the following equations, your answers may be complex. a. x 0 x x. The graph below represents the graph of a function f. a. Evaluate f(). Determine all values of x that produce f(x) =. Determine the domain of f using interval notation. Determine the range of f using interval notation.. Find the domain and range (in interval notation) of each of the following graphs of relations, and determine if that relation is also a function: a.. Given the quadratic function a. the y-intercept the x-intercept(s) the vertex q x x x find:. The height of a softball being hit is given by the function h t t t where h is the height of the ball (in feet) and t is the number of seconds after the ball has been hit. a. After how many seconds does the ball reach its maximum height? What is the ball s maximum height? How much time passes before the ball hits the ground? Round your answer to the nearest hundredth of a secon

5 . Solve the equation. a. a a x x n n n n n n n n n n ( )( )( ) w w e. y. Perform the indicated operations and simplify. Rationalize denominators where appropriate. 0 a. 7 x y x xy e. f. v v 7. Solve the equations below for b r a. w w c b a. Simplify the following using only positive exponents in your answers. Assume all variables represent positive real numbers. a. v e. y y 7n n w w xy z x y z f. x y z ANSWERS. a. xy x y nm xx x yx e. y x y f. z7z g. nm h. 7c d c d i. m pm 0mp p j. vv k. x y zx y z. a. x or x x or x x or x

6 . a.,,,,, e., f., g.. a.,,,,. a.. a. x 7 or x x or x x 7 or x x or x 7. a.,,,. 0.7 miles. a. n 0. a. p or p. a. 77 m x or x 7 a b or b. a. i w or w. The southbound airplane is travelling at 00 mph; the eastbound airplane s speed is 0 mph. a. m m x y x y a b c d w c d w c b w

7 . a. x x x 7 x. a. 7. a. A m e. kb k n m y p a f. 7 g. kx w z h. 0 i. x j. 7. a. 7 or 0.0 D.0v 7. feet mph. a. i 7 i i 0. a. x i or x i x i or x i f. or x (The function doesn t include x ). a. 0 x D:, R:,. a. Domain:,,,,, Domain: 0, Domain: 0, Range:,,0,,,., It s a function Not a function It s a function Range: Range:,0 ;,0. a. 0,, 0 0. a.. seconds feet. seconds. a. a x n w 0 e. y. a. 0 e. f. v 7. a. w b w r or w rw r b w (equivalent answers) c a b or ac c b (equivalent answers). a. 0 y w v e. n f. yz x