Answer Key Name: Date: UNIT #9 ROOTS AND IRRATIONAL NUMBERS REVIEW QUESTIONS Part I Questions. Which of the following is the value of 6? () 6 () 4 () (4). The epression is equivalent to 6 6 6 6 () () 6 () 6 () (4) 6 4 6 (). If f 4 then f () 8 () 6 () 6 (4) 4. Which of the following is an irrational number? f 4 f 4 6 4 6 () () () () 4 9 (4) 8 The ratio of integers is a rational number. The square root of any nonperfect square will be an irrational number. So, choice () is irrational. (). Which of the following sums would represent an irrational number? () () 49 4 () (4) The sum of two rational numbers will be rational. But, the sum of a rational and irrational number will be irrational. () is the only eample of this. () emathinstruction, RED HOOK, NY 7,
6. Given the function g 4, which of the following values of cannot be in the domain of g? () () () (4) The domain is the set of -values that give outputs. But, we cannot find the square root of a negative number. When we substitute = -, we are forced to find the square root of -. Which we cannot do. () 7. The function f a b is graphed on the grid below. Which of the following is the sum of a and b? () 7 () () (4) The is a shifted version of y by 4 to the left and up. So, its equation is f 4, so a 4 and b, thus ab. (4) 8. Which of the following is the solution set to the equation? (), (), () 7, (4), 9. The solution set to 4 is () 4 () 4 4 () 6 (4) or 7 4 4 4 4 4 4 4 4 () (). Over which of the following intervals is the function f always increasing? () () () (4) This function is a shift of y by units right and units down, giving the graph below. From this we can see it increases for all inputs () emathinstruction, RED HOOK, NY 7,
. Which of the following equations has the same solutions as? () () () (4) (). When solving the equation using the method of completing the square, which of the following quantities must be added to form a perfect square trinomial? () 4 () 8 () (4) 4 Whenever we complete the square on a trinomial of the form y b c we always add on the square of half of b, i.e. b, which in this case is (). Which of the following represents the solutions to the equation 64? () 4 and 6 () () (4) 64 6994 () 4. The positive solution to the quadratic equation 6 is () 6 () () 6 (4) 4 6 6 9 9 8 9 (4). If f 6 then f () 4 () () 8 (4) f f 6 6 86 6 4 () emathinstruction, RED HOOK, NY 7,
Free Response Questions 6. Graph the function f on the grid below. Show the table that you created by hand or using your calculator. Then, state its domain and range. Table: - - 6 y - Domain: Range: or, y or, 7. Give an eample of a non-integer rational number and an irrational number. Non-integer Rational Eample Irrational Number 4 If you added your two numbers, would the sum be rational or irrational? The sum would be irrational. Any time a rational and an irrational number are added the result is irrational. 8. The graph of f is shown below along with the graph of g. g. Determine a formula for the function f y g Clearly, the function g is a shift of the function f by units to the right and units down. So, g will have the formula: g emathinstruction, RED HOOK, NY 7,
9. Solve the following equation for all values of. 8 8 9 9 8. Solve the following equation for all values of. Epress your answers in simplest radical form. 7 6 7 7 9 9 4 7 6 4 4 9. Solve the following quadratic equation for all values of using the method of completing the square. 8 866 86 4 8 4 4 4 4 4 4. Algebraically determine the solutions to the equation shown below. Round your answers to the nearest hundredth. 4 6 6 6.7748.77 6 6.446.44 6 emathinstruction, RED HOOK, NY 7,
. The parabola y is shown graphed. Algebraically, find the value of the positive zero of this function. Epress your answer to the nearest tenth. y a, b, c 4.6. 4. Evin graphs the parabola y 4 7 and finds that it has no -intercepts. Eplain how you can verify Evin's result algebraically by solving for the zeroes of the function. 47 4 4 4 7 4 Since we cannot find the square root of a negative number, there must not be any real zeroes.. Consider the function f. (a) Graph the function on the aes to the right. - - - 6 y - - (b) Over what interval is f? All values where the graph is above the ais: emathinstruction, RED HOOK, NY 7,