()+k and graph it. Also, state the Rational Functions in Order to of Turn write the function in the form g(x) = a (x_) + k and graph it. Also, state the domain and range using inequalities. 1. g(x) = 3x48 x+2 46 6 x Amy has purchased a basic letterpress kit for $140. She plans to make wedding invitations. She estimates that the cost of the paper and envelope for each invitation is $2. Model this situation with a rational function that gives the average cost of a wedding invitation when the cost of the kit is included in the calculation. Use the graph of the function to determine the minimum number of invitations that brings the average cost below $5. 2. Given C(w) = represents the average cost in dollars of a w 1 00 wedding invitation when the cost of the kit is included, graph it using key features. Average cost (dollars) - NWAVIA 0 Then select two choices that are true about the function C(w) 20 40 60 80 A There is a zero at 2. Number of invitations B There is an asymptote at x = 0. C There is an asymptote at y = 2. D There is a y-intercept at 2. A "zero" implies an x-intercept. 4lifelong Algebra 2A LEP 4 L4L - Algebra 2A (2020) Page | 13.ewrite the function in the form using inequalities. 9-XZ- SIAXE EVALUATE Independent Practice Lesson 8.1 Homework Complete problems 1-4 for independent practice. When you are finished, check the solutions with your teacher. Identify the transformations of the graph of f(x) = = that produce the graph of the given function g(x). Then graph g(x)on the same coordinate plane as the graph of f(x) by applying the transformations on the asymptotes x = 0 and y = 0 to the reference points (-1, -1) and (1, 1). Also, state the domain and range of g(x) using inequalities. 1. g(x) = 2(1) -2 2. g(x) = 2x-7 Rewrite the function in the form g(x) = a-+ k. Also, state the domain and range using inequalities. 3. g(x) = =4x+11 x +1 4lifelong Algebra 2A LEP 4 L4L - Algebra ZA (2020) Page / 14duce the graph of ions with your teacher. write the function in the form g(x) = a (x-;) + k and graph it. Also, state the domain and range using inequalities. 4x+15 4. -2x-6 Optional: Complete problems 1-15 odd from your textbook on separate lined paper, When you are finished, check the odd problems for solutions at the back of the textbook. lifelongGiven that the model C( p people when there is a graph represents C(p). Graph EVALUATE Independent Practice Lesson Reflection (Circle one, Starting... Getting there... Got it Learning Goal I can find the key features of a rational function and then graph the function using zeros, asymptotes, and end behavior. Once you have completed the above problems and checked your solutions, complete the Lesson Checkpoint Lesson 8.1 Checkpoint below . Complete the Lesson Reflection above by circling your current understanding of the Learning Goal. 1. Which function is graphed to the right? A. F(x) =+3 O B. f(x) = 2(+2) 57 + 3 c. f ( x) = 1+ 2 - 5 2. Graham wants to take snowboarding lessons at a nearby ski resort that charges $40 per week. The resort also charges a one-time equipment-rental fee of $99 for uninterrupted enrollment in classes. The resort requires that learners pay for three weeks of classes at a time. The function f(x) represents the situation f (x ) = 40x + 99 Select two choices that are true about the function f (x). A There is a zero at 0. O B There is an asymptote at y = 40. C There is an asymptote at x = 0. D There is a vertical shift up 99 units. lifelong Algebra 2A LEP 4 L4L - Algebra 2A (2020) Page / 16neckpoint on is graphed to the right syisgives, and end behavior. Independent Practice set of a rational function and then graph the ipleted the above problems and checked your s above by droing, your currer Lesson Reflection (Circle one) Starting. Getting there.. Got it! the Lesson Checkpoint Given that the model C(P) = p + 50 represents the total cost C (in dollars) for each person in a group of p people when there is a shared expense and an individual expense, select Yes or No to indicate which graph represents C(p). Yes No Graph Total Cost 10 15 20 25 30 35 40 4 People Total Cost 10 15 20 25 30 35 40 45 50 Total Cost 10 15 20 25 30 35 40 45 39 5 lifelong Algebra ZA LEP 4 L4L - Algebra ZA (2020) Page | 17using interval notation. intercepts, and "holes." Also, sketch the graph of the ratio. EVALUATE Independent Practice Lesson 8.2 Homework Complete problems 1-6 for independent practice When you are finished, check the solutions with your teacher. Find the rational function's asymptotes, x-intercepts, and "holes." Also, sketch the graph of the rational function. Then list the domain and range using interval notation. 1. f (x ) = 2+ x -2 2. f (x) = 2+2x-3 -8 -5 4 -3 - 2 -1 0 lifelong Algebra 2A LEP 4 L4L - Algebra ZA (2020) Page / 25tical asymptote at x has no asymptotes. Select which statement of the following rational function Once you have completed the above problems and checked Complete the Lesson Reflection above by circling your cun I can find the key features of a rational function and then graph the EVALUATE Independent Practice function using zeros, asymptotes, and end behavior. Lesson 8.2 Checkpoint below. Learning Goal 3. State the point of discontinuity, i.e., "hole," of the function Use the rational functions below to answer the following questions -3x2 - 12x * = f( x) =x2+5x+4 4. Identify the x-intercept of the function. 5. Find the vertical asymptotes, if any, of the function. * = Determine which of the following graphs is the graph of the given function. 6. f(x) = x2-5x-6 6 7 ' 2 3 4 5 6 Optional: Complete problems 7-11 odd from your textbook on separate lined paper. When you are finished, check the odd problems for solutions at the back of the textbook. lifelong Algebra ZA LEP 4 L4L - Algebra ZA (2020) Page / 26EVALUATE Independent Practice How I Did (Circle one) Learning Goal I can find the key features of a rational function and then graph the Starting... Getting there.,, Got it! function using zeros, asymptotes, and end behavior. Lesson 8.2 Checkpoint " Once you have completed the above problems and checked your solutions, complete the lesson checkpoint below. Complete the Lesson Reflection above by circling your current understanding of the Learning Goal. Select which statement of the following rational functions given is true. 1. f(x) = 7+3 A. The graph has no asymptotes. B. The graph has a vertical asymptote at x = 2. O C. The graph has a horizontal asymptote at y = 3. 2. g(x) = 2 -9 A. The graph has no asymptotes. O B. The graph has a vertical asymptote at x = 2. C. The graph has a horizontal asymptote at y = = Use the rational functions below to answer the following questions 3. State the point of discontinuity, i.e., "hole," of the function. f (x) - 2x2 - 4x x = x2 - 4 4. Identify the x-intercept of the function. 5. Find the vertical asymptotes, if any, of the function. x =_ lifelong Algebra 2A LEP 4 L4L - Algebra 2A (2020) Page |27lifelong Algebra ZA 9AXE = ( x ) / LEP 4 ( 2+x)x Determine which of the following graphs is the graph of the given function. L4L - Algebra ZA (2020) Page 1 28 Lesson 9.1 Adding and Subtr Expressions Learning Goal: I can describe the similarities between the set of rational numbers and rational expressions. I can add and subtra rational expressions. (Standard A-APR.D.7) EXPLORE Identifying Excluded Val 0 Read Explore Parts A-F and complete the following activit (1 -x) of the expression is X - 1ed from Lesson 9.3). " uonerbs up jo suonngos value will be an extraneous solution through by the LCD and solving ahue of the original equation is a solution the information about the excluded uations Algebraically he steps are done for you. In your own words, explain the reasoning behind each step. 2. 1+= = 5X Step Work Reason 1 x *0 2 1 . 7 + 5 - 5x 3 5x 5 _ 1 5x $ 5x 5x 4 5x + 5 1 5 x 5 x 5 5x (5x + 5) = 5x 6 25x2 + 25x = 5x 7 25x2 + 20x = 0 18 5x (5x + 4) = 0 9 x = 0, x = - 10 The solution is ONLY x = lifelong Algebra 2A LEP 4 L4L - Algebra ZA (2020) Page 14