1. Graph the function f(x) = (x + 3)3 by hand and describe the end behavior. (1 point) The Function is cubic so it ends in opposite directions‚ the left side will go down and the right side up since the first coefficient is positive. 2. Graph the function f(x) = –x4 – 4 by hand and describe the end behavior. (1 point) The function is quartic so the left and right end will continue in the same direction‚ the lead coefficient is negative so both sides will go down. 3. Graph the function f(x) =
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1. A line passes through the points (–3‚ –3) and (–1‚ 3). What is the slope of the line that passes through the two points? Hint X -3 -1/3 3 1/3 2. A line passes through the points (3‚ –4) and (7‚ 12). What is the y-intercept of the line? Hint X (0‚ 4) (4‚ 0) (0‚ –16) (–16‚ 0) 3. Consider the following system of equations. y = 8x - 8 y - 8x = 7 What can you conclude about the system of equations? Hint X The system of equations is inconsistent. The system
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Quadratic Equations ax2 + bx + c = 0 Examples of Quadratic equations 1. x2 +2x – 8 = 0 2. x2 – 10x + 25 = 0 3. 3x2 + x - 2 = 0 Quadratic Formula If [pic] a x2 + b x + c = 0‚ then [pic] Finding the zeros of the quadratic functions - The zeros of a function are the input values which result in an output value of zero. One way of solving quadratic equations is using factoring Examples are the following: 1) x2 + 5x + 6 = 0 Set this equal to zero:
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1. What is the exact number of bits in a memory that contains 640M bits? 640 · 1024 = 655‚360 · 1024 = 671‚088‚640 bits. 2. How many bits are in 1 Tb? You are asked to figure out the exact result. Hint: Depending on the tool used to calculate this‚ you may need to use a trick to get the exact result. Note that 220 = 1‚000‚00010 + d‚ where d is the difference between 220 and 1‚000‚00010‚ and that 1T = (1‚000‚00010 + d)2 8 bits/byte => 8 · 1 trillion or 812 => 8‚000‚000‚000‚000 3. Convert the binary
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Now it is your turn to plan the trajectories required to launch a spacecraft through a specific route in space. The launch area is identified on the map below. Select three points for your spacecraft to travel through and label them Point A‚ Point B‚ and Point C. A coordinate plane is shown with a point at 1‚ 2 labeled‚ Launch Area. Log the coordinates of the specific points in space to which your spacecraft will travel. Please remember to include the graph of your points and the lines connecting
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following relational database: employee(employee-name‚ street‚ city) works(employee-name‚ company-name‚ salary) company(company-name‚ city) manages(employee-name‚ manager-name) For each of the following queries‚ give an expression in relational algebra‚ tuple relational calculus‚ and domain relational calculus: a. Find the names of all employees who work for First Bank Corporation. b. Find the names and cities of residence of all employees who work for First Bank Corporation. c. Find
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PROPORTION METHOD The proportion method is used in both of these expressions. A proportion is an equation that says that two ratios are equivalent. The use of cross multiplying is in use in both expressions as well. I believe the first expression (#56) uses the extreme-means property; the product of the means is equal to the product of the extremes. #56. To estimate the size of the bear population on the Keweenaw Peninsula‚ conservationists captured‚ tagged‚ and released 50 bears
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Summer 2010-3 CLASS NOTES CHAPTER 1 Section 1.1: Linear Equations Learning Objectives: 1. Solve a linear equation 2. Solve equations that lead to linear equations 3. Solve applied problems involving linear equations Examples: 1. [pic] [pic] 3. A total of $51‚000 is to be invested‚ some in bonds and some in certificates of deposit (CDs). If the amount invested in bonds is to exceed that in CDs by $3‚000‚ how much will be invested in each type
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CBSE TEST PAPER-01 MATHEMATICS (Class-10) Chapter 3 : Pair Linear Equations in Two Variables 1. 2. 3. 4. For which values of p does the pair of equations given below have unique solution? (2 marks) 4x + py + 8 = 0‚ 2x + 2y + 2 = 0 Solve graphically: 3x + 2y = 14x‚ x – 4y = 7 (3 marks) Two rails are represented by the equations x + 2y – 4 = 0 and 2x + 4y -12 = 0. Represent this situation geometrically. (3 marks) a b c On comparing the ratio 1 ‚ 1 and 1 find out whether the lines representing the
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Welcome to Oakville Lake Amusement Park! As one of the new roller coaster engineers‚ you have been tasked with developing a roller coaster that will intertwine with existing Oakville Lake Amusement Park structures. For one of the more thrilling sections‚ the roller coaster will dive down in-between buildings‚ plummet underground‚ pop back up‚ and coast over a hill before shooting back underground. There must be three distinct points where the roller coaster crosses the x–axis. Precise measurements
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