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## REVIEW TEST 1

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**1. Find the slope of the line determined by (3, -1) and (5,**7). A. - 4 B. 4 D. - 1/2 C. 1/2 E. None of the above**Sorry, that answer is incorrect.**Remember slope is defined by Where x1 and y1 are the coordinates of the first point. Please try again. Please click here to try again.**Great, the correct answer is 4, since -**Please click here for the next question.**2. Find the slope of 3x + 2y = 18.**A. 3 B. - 3 D. 2/3 C. -3/2 E. None of the above**Not quite, that answer is incorrect.**Remember to find the slope you solve the equation for y and the slope is the coefficient of the x term – y = mx + b Please click here to try again.**Hey great, the correct answer is - 3/2, since**y = - 3/2 x + 9 And the coefficient of x is the slope. Please click here for the next question.**3. Find the y-intercept of 3x + 2y = 18.**A. 6 B. 18 D. 9 C. - 6 E. None of the above**Too bad, that answer is incorrect.**Remember to find the y-intercept you solve the equation for y and the y-intercept is the b term – y = mx + b Please click here to try again.**OK, the correct answer is since 9 since**y = - 3/2 x + 9 And the constant term is 9. Please click here for the next question.**4. Find the domain of**A. x 7 B. x > 7 D. x 7 C. x ≠ 7 E. None of the above**Not quite, that answer is incorrect.**Remember you may not take the square roots of negative numbers. Hence the interior of the square root sign must be positive. Solve for x in x – 7 ≥ 0 Please click here to try again.**Terrrrriffffic, the correct answer is x 7,**Since x – 7 ≥ 0 means x 7 Please click here for the next question.**5. Find the domain of**A. x ≠ 4 B. x > 4 D. x < 4 C. x ≠ - 4 E. None of the above**That answer is incorrect. It is a hard one!**Remember you may have a zero in the denominator. Hence x – 4 ≠ 0. Please click here to try again.**Terrrrriffffic, the correct answer is x ≠ 4 ,**since the denominator may not be 0 and it is when x = 4. Please click here for the next question.**6. Considerf (x) = x 2 + 2x – 1and find the x-intercepts.**A. x = 0 and x = 2 • x = - 0.41 & x = 2.41 C. x = 0.41 and x = – 2.41 D. x = - 2 & x = 1 E. None of the above**Sorry that answer is incorrect.**There are at least three ways to find the x-intercepts: 1. Factor the quadratic and solve the two factors. (This one does not factor easily.) 2. Use the quadratic formula. 3. Graph it on our calculator and use ZERO under the CALC menu. Please click here to try again.**Yes, the correct answers are –2.41 and 0.41.**I used my calculator and ZERO under the CALC menu. Please click here for the next question.**7. Considerf (x) = x 2 + 2x – 1and find the y-intercept.**A. y = 0 • y = 0.41 C. y = – 2.41 D. y = - 1 E. None of the above**Too bad that answer is incorrect.**There are at least three ways to find the y-intercepts: 1. Let x = 0 and solve for y. 2. Use the fact that the y-intercept = c in the original equation. 3. Graph it on your calculator and use VALUE under the CALC menu with x = 0. Please click here to try again.**OK, the correct answer y = - 1.**I used the fact that C = - 1 in the original equation. Please click here for the next question.**8. Considerf (x) = x 2 + 2x – 1and find the vertex.**A. x = - 1 and y = - 2 • x = - 1 & y = 2 C. x = - 2 and y = – 1 D. x = - 2 & y = 1 E. None of the above**No that answer is incorrect.**To find the vertex: 1. Use the formulas: 2. Graph it on our calculator and use MINIMUM under the CALC menu. OR Please click here to try again.**Correctamundo, the answer is (- 1, - 2).**I used my calculator and MINIMUM under the CALC menu. NOTE: You will need this answer for the next question. Please click here for the next question.**9. Consider f (x) = x 2 + 2x – 1 and find the maximum**or minimum value, whichever exist. Identify it as either a maximum of minimum. A. A maximum of - 2 • A maximum of 1. C. A minimum of – 2. D. A minimum of 1. E. None of the above**No that answer is incorrect.**To find the maximum or minimum use the results of the previous question. Please click here to try again.**Yes, the answer is a minimum of - 2.**See the results of the previous question #13. Please click here for the next question.**10. A bit of pre-calculus now!If f (x) = x 2 – 5x + 3,**find f (x + h).Please simplify your answer. A. (x + h) 2 – 5 (x + h) + 3 B. x 2 + h 2 – 5x + 5h + 3 C. x 2 + 2xh + h 2 – 5x – 5h + 3 D. 3 E. None of the above**That answer is incorrect. It is a hard one! You must**substitute correctly. Remember that f (x + h) means that you are to substitute an x + h everywhere an x appears in the equation. In this problem substitute an x + h for x into x 2 – 5x + 3. Don’t forget to simplify Please click here to try again.**That answer is correct but you forgot to simplify!**Please click here to try again.**Grrrrreat, the correct answer is**x 2 + 2xh + h 2 – 5x – 5h + 3, since (x + h) 2 - (5) (x + h) + 3 = x 2 + 2xh + h 2 – 5x – 5h + 3. NOTE: You will need this answer for the next question. Please click here for the next question.**12. Let’s complete that idea.If f (x) = x 2 – 5x + 3,**find the difference quotient.Please simplify your answer. A. x 2 + h 2 – 5x – 5h + 3 • 2x + h – 5 D. 2xh + h 2 – 5h C. 3 E. None of the above**That answer is incorrect. It is a hard one! This is an**important question. Remember that the difference quotion is, i.e. you need to divide the answer for question 11 by h. Please click here to try again.**That answer is incorrect. It is a hard one! This is an**important question. Remember that the difference function is, You forgot to do the final step and divide the difference by h. Please click here to try again.**WOW, the correct answer is indeed 2x + h – 5.**NOTE: You will need this answer for the next question. Please click here for the next question.**13. If f (x) = x 2 – 5x + 3, find the slope of the secant**line joining (0, f(0)) and (3, f(3)). A. m = - 2 • m = - 1 D. m = 1 C. m = 3 E. None of the above**Sorry that answer is incorrect.**Remember to find the slope of the secant you can do either of the following: 1. Work out the y values of the two points given and use the slope formula OR 2. Substitute x = 0 and h = 3 into the result of question 12. Please click here to try again.**Great, Substitute x = 0 and h = 3 into**2x + h – 5 yields 0 + 3 – 5 = - 2 Please click here for the next question.**14. If f (x) = x 2 – 5x + 3, find the equation of the**tangent line at (2, f(2)). A. y = x + 1 B. y = - 2x - 1 C. y = - x - 1 D. y = - 2x + 1 E. None of the above**No that answer is incorrect.**Use your calculator and the DRAW menu using TANGENT. Please click here to try again.**Yes Yes Yes, the correct answer is y = - x – 1.**I used my calculator and the DRAW menu using TANGENT. Please click here for the next question.**15. Find the following limit.**A. 2 • 3 C. 1 D. - 1 E. None of the above**Sorry that answer is incorrect.**Most of the time to find the limit you can just substitute the value x approaches. In this case substitution will work. Try it. Please click here to try again.**Yes, the correct answer is 1.**Substituting 1 for x yields Please click here for the next question.**16. Find the following limit.**A. 1 • - 1 C. Undefined D. 0 E. None of the above**Too bad that answer is incorrect.**Most of the time to find the limit you can just substitute the value x approaches. In this case substitution will work. Try it. Please click here to try again.**OK, the correct answer is 0.**Substituting 2 for x yields Please click here for the next question.**17. Find the following limit.**A. 3 • Undefined C. 0 D. 1 E. None of the above**No, that answer is incorrect.**Most of the time to find the limit you can just substitute the value x approaches. In this case substitution will not work since you get 0/0 for your answer. You must factor the numerator and denominator and cancel common factors before you substitute 3 for x. Please click here to try again.