1.   Simplify (3x^1/2y^3/4)²
     

2.   Rationalize the denominator of the expression given below and simplify.
     

3.   Factor x² - 19x + 90
     

4.   Factor 9x² - 4y⁶
     

5.   Add the rational expressions given below.
     

6.   Write the complex fraction given below in standard form by multiplying by the conjugate top and bottom.
     

7.   In the first few years after purchase, the value of a car that is worth $20,000 new is given by V = 20000 - 2800t where t = number of years after the car is purchased. If such a car has a value of $12,500 , how long ago was it purchased? Round to the tenth of a year.
     

8.   Solve the equation x² = 5x + 2 with the quadratic formula.
     

9.   A box has a height of 2 feet and a length that is 3 ft more than its width, as shown below. If the volume of the box is 14 cubic feet, what is the width and length? Round answer to 2 decimal places.
     

10.   Solve 3x^4/3 + 3 = 51
     

11.   Solve the radical equation below. You must show the algebraic solution - not just check and guess!
     

12.   Solve the absolute value inequality given below.
     

13.   Solve the rational inequality shown below using the critical value method.
     

14.   The number of inches per hour I that drain from a pool varies directly as the square of the diameter D of the hose used. If a 3/4" diameter hose is used, I = 0.9 inches per hour. How many inchese per hour I will drain with a hose of diameter D = 2.5". Round values to 2 significant decimal places.
     

15.   A circle has endpoints of a diameter as shown below. What is its equation?
     

16.   Graph the equation given below and show ALL intercepts.
     

17.   Find the domain of the function given below.
     

18.   A backyard has dimensions as shown below. Give the function for its area. Then use this function to find the width x for a backyard with area of 500 square feet. Round to 2 places.
     

19.   A person sells 180 units per day and makes a daily net profit of $10. If 300 unit are sold per day the daily net profit is $30. Assuming a linear relationship between sales (x) and profit (y), find the equation that relates units sold per day (x) and net daily profit (y).
     

20.   The price P of an item is a function of x, the number of items produced daily, and is given by the formula P = 0.02x² - x + 20. What number of items x results in the lowest price?
     

21.   Sketch the graph of f(x) = 2(x + 3)² + 2. Show the vertex and at least two other points.
     

22.   Sketch the graph of g(x) = ½ f(x), given the graph shown below.
     

23.   The graph of y = x³ and a shift of this graph are shown below. Identify the formula of the shifted graph.
     

24.   Given f(x) = x² + x, evaluate and simplify the difference quotient expression given below.
     

25.   Find the inverse of the function f(x) given below. Also, show that (f o f ^-1)(x) = x and (f ^-1 o f)(x) = x.
     

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