PRE-CLASS ASSIGNMENT Sections 3.5, 3.6 Name; Print and complete this assignment. This assignment must be submitted on Canvas. Late submissions will not be accepted. It is essential you do this assignment so you can participate and understand the in-class group activities. You can use your textbook, internet, LAs, teamwork, etc.; however, copying another student's work will be considered cheating and dealt with accordingly. Q1. Video: Behavior of a rational function (https://youtu.be/MimV3kqV5Kw) a) Explain in your own words the meaning of the following symbols: x -> q V - - 00 Explore the behavior of points on the graph of f (x) = when x - 2- x - 2 Go to https://www.desmos.com/calculator/cvqq31yg3m and, using the slider, move the point on the graph. Note the coordinates of the point. Write your conclusions below: As x - 2 , y values The points on the graph comes closer and closer to the line b) Repeat similar analysis when x is greater than 2. You will need the following notation: x - q means x values approach q from the right or through values that are greater than q x -> too means that x values increase without bound, that is they can be arbitrarily large. (i) Use a calculator to complete the table: x y = - (ii) In your own words, describe the x - 2 2.1 behavior of x values: 2.01 2.001 (iii) Use symbols to describe behavior of x: x -> 2.0001 2.00001 (iv) In your own words, describe the behavior of y values: (v) Use symbols to describe behavior of y: y - (vi) Summarize the findings in a sentence: as x - then y -(vii) Use the table of values to plot the points on the graph of f(x) Describe how the points on the graph behave when x -> 2+ pool 281 21 Q2. Draw a graph of a function that has given properties. First example was done for you. a) When x - 2- then y - too and b) When x -> 2" then y - too and when x - 2* then y - too . when x -> 2* then yoo. Q3. Consider function f (x) = - 5x x + 1 ' . Now, you will investigate what happens to values f(x) when x - too andx- -co. a) Complete the table. Use a calculator; write the decimal until first nonzero digit X y = SX 5x y = x +1 x + 1 10 -10 100 100 1000 1000 10,000 10,000 100,000 100,000b) Write your conclusions using the arrow notation. When x- too then y -> When x -> -0o then y -> c) Plot the points in the coordinate system below. Write down your observations: When x -> too, the points on the graph When x - -0o, the points on the graph_ Q4. a) Use the graph to complete the statements below When x - -3- then y - When x - -3+ then y - When x - 3- then y - When x - 3+ then y - When x - -0o then y - When x - too then y - b) A horizontal line y=a is a horizontal asymptote for f(x) if y -> a when x -> too or when x - -00 Does the graph above have a horizontal asymptote? If yes, what is its equation? c) A vertical line x = a is a vertical asymptote for f(x) if y -> too or -co when x -> a* or x -> a Does the graph above have a vertical asymptote(s)? If yes, what is its equation? 07, In chapter , you were a Formulas, For couimple.25. Video: (Solving an inequality graphically (https://goo.8//0a6vdC); Video: Solving a quadratic inequality graphically (https://goo.gl/uiyaxk) a) The graph of a function f (x) is given below. What are the solutions of the inequalities below: Write them in the interval notation . (i) The solution of f (x) > 0 is 1- NW (ii) The solution of f (x) SO is Q6. Recall that when we multiply two numbers we have the following: Positive # . positive # = positive # Negative # . negative # = positive # Positive 3 . negative 3 = negative # a) Without performing calculations, determine whether the number 30 ( - 4 ) . ( - 2 ) 0 ( - 1 ) 2 0 7 is positive or negative. Explain your reasoning. b) Let f (x) =-2(x+3)(x-2)(x2 +1). Since f(-4) =-2(-4+3)(-4-2)((-4)2+1) =-2(-1)(-6)(17). Determine whether f(-4) is positive or negative without performing multiplication. c) Using technique from part b), determine whether f - is positive or negative. Q7. In chapter 2, you were asked to find the domains of functions that had a square root in their formulae. For example, to find the domain of f(x) = V2.x - 7 , we had to make sure that 2x - 7 is notnegative, as square root of a negative number is not a real number. So, to find the domain we had to solve the inequality 2x - 720. Write an appropriate inequality that should be used to find the domains of functions below. Do not solve. a ) f (x ) = V2x3 - 5x2 - 3x x must satisfy the inequality: b ) 8 (s ) = 13x + 4 x 2 - 5 x must satisfy the inequality