3 e) x f) 2. Precalculus Worksheet P Complete the following questions from your textbook: p11: # Why would you never write 5 < x > 7?


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1 Precalculus Worksheet P.1 1. Complete the following questions from your tetbook: p11: #5 10. Why would you never write 5 < > 7? 3. Why would you never write 3 > > 8? 4. Describe the graphs below using both inequalities and interval notation Later in the course we will be using sign charts. Sign charts are simply number lines with + or signs on them to represent whether or not the function or equation is positive or negative on that interval. Suppose the sign chart below represents when the function f () is positive or negative. Use the sign chart to answer the questions 5 and 6 in interval notation. 5. When is f () < 0? f () If f () = 0 when =, but not when = 7, when is f () > 0? 7. Use both inequality AND interval notation to describe the set of numbers. Define any variables used. a) In Ecel, you can create an ifthen statement that will enter a specific value or tet into a bo depending on given conditions. Suppose you would like to enter a value of YES into cell A8 if the value in cell A7 is between 4 and 16 including both. b) A programmer wants to create an alertbo if the user inputs a value that is at least Identify the base in each of the following epressions, then evaluate each epression. a) 4 b) 4 c) 3 3 d) 3 3 e) 1 f) 1 9. Complete questions 47 5 from page 1 in your tetbook.
2 10. Match the following equations with the property illustrated. Each letter is only used once. ( 3) y= 3( y) ab= ba ( ab) ab+ = 0 ( + 3) + 0= ( + 3) a( + y) = a+ ay 1 ( + ) = 1 ( + ) 1 ( + y) = + y A) Commutative Property of Addition B) Commutative Property of Multiplication C) Associative Property of Addition D) Associative Property of Multiplication E) Identity Property of Addition F) Identity Property of Multiplication G) Inverse Property of Addition H) Inverse Property of Multiplication I) Distributive Property ( a+ b) + c= c+ ( a+ b) ( ) ( ) y+ z+ a = y+ z + a Simplify each epression. a) 4 3 b) 3a a 5b y a Many times we need to undo the distributive property. This is the beginning of factoring. When you undo the distributive property, we say you have factored out the greatest common factor. 1. Factor out the GCF from each epression. a) 3 6y b) c) Describe in your own words what the phrase Take out a GCF means.
3 Precalculus Worksheet P. 1. What is the distance formula? Use it to find the distance between the points (5, 19) and ( 3, 7).. What is the midpoint formula? Use it to find the midpoint between the points (5, 19) and ( 3, 7). 3. Suppose the center of the circle is (4, 3) and another point on the circle at ( 6, ). Write the equation of the circle. 4. Consider the equation ( ) y = 13. a) What is the center and radius of the circle? b) Graph the circle. Find all points on the circle that have a yvalue of 3.
4 5. Consider the equation of the circle ( + ) + ( y 4) = 9. a) What is the center and radius of the circle? b) Graph the circle by hand. c) Is the point ( 1, 6) inside or outside the circle? PROVE it algebraically. d) Use your graphing calculator to graph the circle. Eplain/Show what you must do in order to make this possible. 6. Suppose the endpoints of the diameter of a circle are (5, 19) and ( 3, 7). Write the equation of the circle.
5 Precalculus Worksheet P.3 1. Complete the following questions from your tetbook: page 8 #15, 18, 19, 1, 4 8. The formula for the perimeter of a rectangle is given by P = L + W. Solve this equation for W The formula for the area of a trapezoid is given by A hb b. Solve this equation for b A formula relating Fahrenheit to Celsius is C F 3. Solve this equation for F A satellite orbiting the planet has a mass m, a velocity v, and a radius from the center of the planet equal to R. The mv centrifugal Force F acting on that satellite is given by the equation F =. Solve this equation for R. R 6. You have scores of 68, 8, 87, and 89 on your first four tests, and you have one more to take. In order to get a B you must have an average between 79.5 and What is the lowest score you could get on your last test in order to get a B. 7. When you solve an inequality, when does the inequality change direction. Eplain why. 8. Complete the following questions from your tetbook: page 9 #38 43, 45, 46, 50, 5, 54 **For each inequality you solve, write your solution in interval notation.
6 Precalculus Worksheet P.4 1. The velocity of a rocket launched when t = 0 was recorded for selected values of t over the interval 0 < t < 80. Acceleration is the rate of change in velocity (a.k.a. slope of velocity). Finding average acceleration between two points can be done by finding the slope between those two points on the velocity function. t (seconds) Velocity (feet/second) Find the average acceleration of the rocket from t = 0 to t = 80. What are the units of measurement?. On a recent trip, you noticed that after hours you were 90 miles from home, but after 5 hours you were 70 miles from home. a) Find the averagee rate of change from your first to your second observation. b) What are the units of measurement? What does the averagee rate of change in your position tell you? 3. So far, we have covered 5 types of linear equations: PointSlope, SlopeIntercept, Standard, Horizontal, & Vertical. Identify whichh form each equation below is in and graph each linear equation on the graph paper provided. ( ) a) y = 31 y b) y= 3+ 4 y c) + 3 y = 6 y d) y = 7 y e) = y
7 4. Consider the line that passes through the point (, 4) and has a slope 3 of . 4 a) Graph the equation below. y b) Write the equation of the line in pointslope form. c) Write the equation of the linee in slopeintercept form. d) Write the equation of the line in general form. e) Write the equation of the line that is parallel to this line andd goes through the point ( 9, 5). f) Write the equation of the line that is perpendicular to this line and goes through the point ( 9, 5). 5. A vertical asymptote occurs in a rational function when the denominator of that function is equal to zero. Consider the 5 function y =. What is the equation of the vertical asymptote? (Remember it s a vertical line!) A horizontal asymptote is the yvalue that a function approaches when gets really, really large (a.k.a. infinity) ). Graph 6 the function y =. Just by looking at the graph, what do you think is the equation of the horizontal asymptote? 37 (Remember it s a horizontal line) 7. Consider the equation 1 + y = 5. 3 a) Eplain why this equation is NOT in standardd form, and then fi it so that the equation is in standardd form. b) Rewrite the equation in general form. c) What W is the slope of this line?
8 8. A line that is tangent to a circle at a point is perpendicular to the radius at that point. Consider the circle of radius 5 centered at (0, 0). Find an equation of the line tangent to the circle at (3, 4). 9. The relationship between Fahrenheit and Celsius temperatures in linear. a) Use the facts that water freezes at 0 C or 3 F, and water boils at 100 C or 1 F (not your recollection of temperature formulas) to find an equation that relates Celsius and Fahrenheit. b) Using your equation, find the Fahrenheit equivalent of 10 C. 10. Find the value of or y so that the line through the pair of points has the given slope. a) Points (, ) and (4, 8) with slope =. b) Points ( 1, 3) and (4, y) with slope = ½. 11. Consider the function y=  7. The tangent line to this curve at the point ( 3, 11) has a slope of 1. This line is called a tangent line to the curve, because it shares a common point and slope at that point. a) Find the equation of the tangent line in slopeintercept form. [Graph both the curve and the tangent line on the same screen on your calculator] b) In Calculus, we will use the tangent line to approimate the value of the function. (in other words we find the yvalue on the line instead of the yvalue on the curve) Use the tangent line to approimate the value of the function when = 1. c) Your answer from part b is called a linear approimation. The error is the difference between the estimated value using the tangent line and the actual value from the curve. Find the error in your approimation. **Optional Do you need more practice? The following questions are in your tetbook. Writing equations of lines in different forms page 40 #1, 13, 15, 18, 0, 1, 3, 5 Parallel or Perpendicular Lines page 41 #41 44 Applications of Lines page 41 #45, 47, 48
9 Precalculus Worksheet Factoring 1. Learning to recognize the difference of two perfect squares is more difficult than factoring them. Factor the following epressions, and write something on this paper that will help you recognize this in the future. a) a 5 b) 16 n. Factor the following quadratic epressions completely: a) b 8b 15 b) y 4y 5 c) 6d 35d 6 d) 10t 19t 6 e) 10c 13c 30 f) 3 p 4p 5p i) 3 r 6r 0r j) 3 1 f 14 f 40 f k) 3 0n 3n 1n l) 4 3 0e 3e 6e 3. Factor the following equations using the grouping method: a) a ay 6 6y b) mp 7m 3p 1
10 **Optional If you would like more practice with factoring, here are some more problems to practice a z e m 5 4 a 6 4z 1 5e 6 3m d 3d 10 5h 5h 60 g 8g n 3n k k 60 a 5a 3 6b b 9s 6s m 19m 15m
11 Precalculus Worksheet P.5 The main purpose of P.5 is for you to be able to solve quadratic functions in the most efficient (quickest) method possible. Graphically 1. Graphically solve the equation Describe your method.. Graphically solve the equation + 4= 4. Describe your method. 3. Solve the equation graphically two different ways keep in mind you should get the same answer(s). a) Solve by finding the intersections. b) Solve by finding the zeros. Numerically 4. Complete the following questions from your tetbook: p51 #35, 36 Algebraically: Factoring 5. Complete the following questions from your tetbook: p50 #1, 3, 6 Algebraically: Etracting Square Roots 6. Complete the following questions from your tetbook: p50 #10, 11, 1 Algebraically: Completing the Square 7. Complete the following questions from your tetbook: p50 #14, 16, 17 Alebraically: The Quadratic Formula 8. Complete the following questions from your tetbook: p50 #19, 3, 4 Keep in mind that for the purposes of quizzes and tests, there will be times that you will be asked to use a specific method. However, in general, you may use whatever method works for you and is appropriate. 9. Complete the following questions from your tetbook: p5 #59, 60 Solving Absolute Value Equations Algebraically 10. Complete the following questions from your tetbook: p51 #39, 41, 4
12 11. Solve the following equations algebraically: a) 5 (  3) + 8= 4+ 5 b)  + = c) 3  = 1 d) 31 = e) (  ) = 3(  4) f) 4 = 6
13 Precalculus Worksheet P.6 For questions 1 4, solve the inequality algebraically. Write your answer in interval notation > ³ < The 16 = 4, but the equation = 16 has two solutions, = 4. The reason for this is the fact that Using this fact, solve the following inequalities: =. a)  9> 0 b) ( ) < Complete the following questions from your tetbook: page 59 #9, 11, 13, 15 try to solve them algebraically, then use your calculator to help solve them graphically. 7. Complete the following questions from your tetbook: page 59 #7, 9
14 8. [Calculator Allowed] The cable company is asked to provide service to a customer whose house is located miles from the road along which the cable is buried. The nearest connection bo for the cable is located 5 miles down the road. (see figure below). house miles Cable connection bo miles 5 miles a) If the installation cost is $100 per mile along the road and $140 per mile off the road, epress the total cost C of installation as a function of the distance (in miles) from the connection bo to the point where the cable installation turns off the road. What values of make sense in this scenario? b) What is the minimum possible cost of the installation, and how far away from the connection bo should the cable installation turn off the road? 9. Complete the following questions from your tetbook: page 59 #34, 38, 46 ( ) b b 10. The verte of a parabola of the form f ( ) = a + b+ c is the point, f ( ) g( ) Find the verte of the function a a = + + without using your calculator. Is this point a minimum or a maimum?
15 Precalculus Worksheet = m = m c  = = 8 c = n = nn ( + ) n n = =
16 = = = y = y+ 8 y 16 y = (  4) 34 ( + 1) 14. Solve for : 1 y = Eplain the difference between the following three problems. Are there any similarities in their solution? a) Write the epression as a single quotient: b) Solve: + = c) Solve: + <
6. The given function is only drawn for x > 0. Complete the function for x < 0 with the following conditions:
Precalculus Worksheet 1. Da 1 1. The relation described b the set of points {(, 5 ),( 0, 5 ),(,8 ),(, 9) } is NOT a function. Eplain wh. For questions  4, use the graph at the right.. Eplain wh the graph
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