# Country Life Versus City Life

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Exam 1 Practice Math 099 1. Answer the following questions using the graph of f below. a) Find f ( 4 ) . b) State the range of f using appropriate set-builder or interval notation. c) Find any x-value for which f ( x ) = −1 . 2. Let f ( x ) = x 2 − 2 and g ( x ) = 3 − x . Find and simplify the following. a) f (3 p ) = b) ( f − g )( x ) = c) ( f ⋅ g )( −2 ) = 3. Find the domain of each function below. Be sure to state your answer using appropriate set-builder or interval notation. a) f ( x) = 3x + 1 x − 3x + 2 2 b) h ( x ) = 13 − 6 x 4. The gas mileage of a specific car is a linear function of the speed at which the car is driven. If the car is driven at a rate of 30 mph, the car’s gas mileage is 35 miles per gallon. If the car is driven at 60 mph, the car’s gas mileage is 20 miles per gallon. a) Use this information to write the gas mileage, m ( s ) , as a function of the speed, s . b) Use your function to determine the gas mileage if the car is driven at a speed of 50 mph. Answer in a sentence. 5. Perform the indicated operation. Simplify your answer as much as possible. a) b) c) y2 + 4 y + 4 3y + 3 ⋅ = y +1 y+2 x x4 ÷ = x2 −1 x + 1 t2 8t − 15 − = t −3 t −3 d) e) 8 2r + = r −5 5−r x 3 + = 2 x + 9 x + 20 x + 5 6. Ellen and Doug have to clean their house. When Ellen does it by herself, it takes 7 hours. When Ellen and Doug work together, it takes 4 hours. How long would it take Doug to clean the house by himself? To get full credit, you must define your variable in words, write and solve a rational equation, and answer the question in a complete sentence. 7. Solve each equation. If no solution exists, write “no solution.” 3 a + 11 a) = a +8 a +8 10 b) x + = 7 x 7 3 5 c) + = 2 2x x +1 2x + 2x 8. Solve each absolute value equation or inequality. Express your answers in setbuilder or