How can you use technology to confirm your answers in Exercises 4043 on page 110? We can make the value of h as -2 Compare f (x) and g (x) with the standard linear equation Answer: Answer: The given equation is: Now, So, m = 0.5 Question 19. By using the above properties, Example of relation that is not a function: Hence, from the above, c. Graph the function using its domain. So, Question 1. g(x) = 3x x + 7 < 5 and x + 7 > -5 It is given that a mountain-climber is scaling a 500-foot cliff y = x 3 or y = -x 3 Hence, from the above, The domain of f (x) is: -10 x 10 3 Question 1. m = \(\frac{5}{2}\) The representation of P (x) and Q(x) in the same coordinate plane is: From part (a), We can conclude that the values of f(x) when x = -4, 0, 3 are: -13, -5, and 1, Question 2. Describe the function in two other ways. y = 84 Answer: Explain the meaning of each statement. The domain is 0, 1, 2, 3, 4, and 5. COMPLETE THE SENTENCE We can conclude that m (x) translates 6 units up from the positive x-axis The representation of the given equation corresponding to the intercepts in the coordinate plane is: Question 5. To understand more about graphing a piecewise function, click here. The company fills A jugs of the first size and B jugs of the second size. y = x + 9 The total cost of tickets = (The cost of the child tickets + The cost of the adult tickets) If the vertical line drawn across at anywhere of the graph intersects the graph at most once, we decide the given graph represents the function. Use patterns that are different from those described in Exploration 1. g = 20 2.5 (6) = 5 For graphing functions, we need to plot its asymptotes, its x and y-intercepts, holes, and a few points on it by constructing a table of values. x = 5 So, 2x = y (9x 3) x < -2 and x > -12 (a) Find the domain of the function. 20 10 So, the given graph represents the function. r 0 Answer: g (x) can b ere-written as g Compare the graph of g to the graph of f. f (x) = x + 3 or f (x) = -x + 7, b. y = (180 4(0) ) / 6 The representation of the given equation in the coordinate plane is: Question 7. The given equation is: COMPLETE THE SENTENCE 4v + 9 5 or -3v -6 Hence, from the above, f(x) = | x 1 | + 2; g(x) = 4 | x 1 | + 8 y = a.f (x) Answer: Where, We can conclude that x = 3 We can conclude that b = 5 f (x) = | x | Now, The representation of the function using its domain in the coordinate plane is: WRITING In Exercises 3942, write a real-life problem to fit the data shown in the graph. f(0) = 2 (0) 5 = 0 5 = -5 (4, -3) does not belong either to the x-axis or y-axis = 4 (4 10 ) We can conclude that the value of the expression for the given value of x is: -7, Question 9. The graph of the function is shown. Answer: Question 26. (5, -12), (5, -9), (5, -6), (5, -3) Explain why h is a function of t. m is the slope-intercept The elevation of the submersible is modeled by h(t) = 500t 10,000. So, Find the value of x, so that the function has the given value. g(x) = x + 3 Hence, from the above, Question 6. d. g(x) = | x + 2 | + 2 Four players can ride in each car. g (x) = 3x + 1 2 Answer: r (x) = \(\frac{1}{4}\)x The graph of You sold a total of $16 worth of tickets to a fundraiser. We can conclude that h (x) translated 4 units away from f (x) towards the positive x-axis. June, July, August, Graphing Linear Functions Maintaining Mathematical Proficiency Page 101, Graphing Linear Functions Mathematical Practices Page 102, Lesson 3.2 Linear Functions Page(111-120), Linear Functions 3.2 Exercises Page(117-120), Lesson 3.3 Function Notation Page(121-126), Function Notation 3.3 Exercises Page(125-126), Graphing Linear Functions Study Skills: Staying Focused During Class Page 127, Graphing Linear Functions 3.1 3.3 Quiz Page 128, Lesson 3.4 Graphing Linear Equations in Standard Form Page(129-134), Graphing Linear Equations in Standard Form 3.4 Exercises Page(133-134), Lesson 3.5 Graphing Linear Equations in Slope-Intercept Form Page(135-144), Graphing Linear Equations in Slope-Intercept Form 3.5 Exercises Page(141-144), Lesson 3.6 Transformations of Graphs of Linear Functions Page(145-154), Transformations of Graphs of Linear Functions 3.6 Exercises Page(151-154), Lesson 3.7 Graphing Absolute Value Functions Page(155-162), Graphing Absolute Value Functions 3.7 Exercises Page(160-162), Graphing Linear Functions Performance Task: The Cost of a T-Shirt Page 163, Graphing Linear Functions Chapter Review Page(164-168), Graphing Linear Functions Chapter Test Page 169, Graphing Linear Functions Cumulative Assessment Page (170- 171), Big Ideas Math Answers Grade 7 Accelerated, McGraw Hill My Math Grade 5 Chapter 9 Lesson 4 Answer Key Use Models to Add Unlike Fractions, McGraw Hill My Math Grade 5 Chapter 9 Lesson 3 Answer Key Subtract Like Fractions, McGraw Hill My Math Grade 5 Chapter 9 Lesson 2 Answer Key Add Like Fractions, McGraw Hill My Math Grade 5 Chapter 9 Lesson 13 Answer Key Subtract with Renaming, McGraw Hill My Math Grade 5 Chapter 9 Lesson 12 Answer Key Subtract Mixed Numbers, McGraw Hill My Math Grade 5 Chapter 9 Lesson 11 Answer Key Add Mixed Numbers, McGraw Hill My Math Grade 5 Chapter 9 Lesson 10 Answer Key Use Models to Add Mixed Numbers, McGraw Hill My Math Grade 1 Chapter 7 Lesson 5 Answer Key Make Bar Graphs, McGraw Hill My Math Grade 1 Chapter 3 Check My Progress Answer Key, McGraw Hill My Math Grade 1 Chapter 3 Answer Key Addition Strategies to 20, McGraw Hill My Math Kindergarten Chapter 7 Review Answer Key. -6x + 0 = -18 Answer: Question 38. a. x + y The linear function m = 55 8.5b represents the amount m (in dollars) of money that you have after buying b books. Answer: g = 20 2.5x a. Graph the function. 3 to the value y is equal to 2. Question 59. Now, To find the y-intercept, put x = 0 Where, The solutions of the given inequality are: Hence, from the above, Compare the given equation with the standard representation of the linear equation We can find the values of x and y by putting the values 0, 1, 2.. g (x) = f (x) + 1 w (x) = \(\frac{3}{5} x\) + 2 y = 2 at x = 0 Drawing such curves representing the functions is known as graphing functions. put the values -2, -1, 0, 1, 2 in the place of x and find the values of f(x) toplot a graph [ Remember you can take any value and any number of values] Hence, from the above, The given table is: = 1375 880 Answer: Question 26. The standard form of the linear equation is: Describe the domain and range of the function. From the above graph, x = 20 / 4 Explain. A function can be represented algebraically. How does the graph in part (a) compare to the graph shown? Now, Hence, from the above, The representation of the given equation along with the x-intercept in the coordinate plane is: Question 12. The given relation is: We know that, Answer: Question 66. The representation of the given function in the coordinate plane is: Question 28. Now, y = 24 / 6 And then we get to x a \(\frac{5}{2}\). f (x) = | x | Answer: The standard representation of the linear function is: If there is any such line, the function is not one-to-one. The representation of the given equation along with the x-intercept in the coordinate plane is: Question 10. Hence, Answer: g (x) = -6x + 4 d. y = -3x + 13 b. Graph the function using its domain. y = mx + c = \(\frac{-1 + 1}{-3 + 4}\) We can conclude that g (x) shrink by 1 unit of the graph of f (x). g (x) = 5x + 1 Then we can apply the following transformations to graph the given function. x = 12 / 6 2y + x = 12 + 8 Match each function with its graph. 2 is. We can conclude that x = 2 f(a) = f (0) = c Hence, from the above, y = | ax | Answer: From 14 to 18 seconds, Graph the equation and interpret the intercepts. The other given function is: The given functions are: p(x) = | x + 1 | 2; q(x) = | \(\frac{1}{4}\)x + 1 | 2 g (x) = \(\frac{1}{3}\) | x 1 | 2 To find the value of y-intercept, put x = 0 y = (-9 0) / 3 We will get, We can conclude that s (x) translates 4 units away to the right side of the positive x-axis. Hence, It tells us when x is 2, then y is going to be equal to negative 2. The values of k so that k become integer is 0, 1, 2, and so on y = -4 | x | The representation of the rectangle after the transformation in the coordinate plane is: Question 55. Hence, b. g (x) = (-4x 2) Answer: b (-2) = 18 0.5 (-2) Hence, f can be writen as f (x) The linear function d = 50t represents the distance d (in miles) Car A is from a car rental store after t hours. y = $9.8 Where, The given table is: Hence, from the above, The representation of the slope and the y-intercept in the standard form of the linear function s: 2y + x = 20 Answer: Question 32. Answer: The given functions are: Reflect the trapezoid in the y-axis. We can conclude that the given table represents a linear function, Question 8. g (x) is translated 2.5 units away from f (x) toward the positive y-axis and h (x) is translated 1 unit away from f (x) toward the positive x-axis. v (t) = 1020t The standard representation of a linear equation is: We can conclude that \(\frac{1}{2}\)x = 4 Hence, 5 | x + 7 | < 25 c. g(x) = x 2 The dependent variable is: y which represents the cost in dollars, b. The slope of the line when the two points are given is: The distance you commuted gradually increases Answer: (x2, y2) = (-3, -1) In a graph, this relation can be represented in a straight line The function y = 60 8x represents the amount y (in dollars) of money you have after buying x movie tickets. Use the Horizontal Line Test. Hence, Copy and complete the table to show the different combinations of tickets you might have sold. We can conclude that g (x) translated 2 units away from f(x) to the left side i.e., towards the positive y-axis, c. The x-intercept of g(x) is: 5 The examples of how m and b varies are as follows: y = 30 + 5x x = -30 / 5 Hence, from the above, The independent variable of the given function is: x We use cookies to ensure that we give you the best experience on our website. Question 25. Question 25. We know that, Answer: Question 34. We can conclude that h (x) is a vertical stretch of f (x), Question 30. This graph does not represent our function if this line intersects it more than once. The slope for a constant function will be 0. y (x) = | 5x 3 | + 4 To find the value of the y-intercept, put x = 0 m = \(\frac{1}{3}\) and b = \(\frac{5}{6}\)k We know that, Hence, from the above, How does the graph of the linear function f(x) = x compare to the graphs of g(x) = f(x) + c and h(x) = f(cx)? A relation is said to be a function if every input has exactly one output So, Hence, b. Graph s. Describe the transformations from the graph of f(x) = | x | to the graph of s. From the above, Hence, Describe the transformation from the graph of C to the graph of T. Hence, from the above, We know that for a relationship to be a function, From part (a), y = mx + c g(0) = 0 1 = -1 The representation of the perimeter of the second isosceles triangle in the coordinate plane is: b. y =2x 4 The result is 33 find the number , in each of the following lines, underline the smallest number and put a ring round the largest number15/3, 12/6, 27/9, 8/2, 10/10, If x= 2 and y=-5, then xy + 4x = The given graph is: 2x y + 6 = 0 Once we have determined that a graph defines a function, an easy way to determine if it is a one-to-one function is to use the horizontal line test. h (x) = \(\frac{1}{2}\)f(x) Hence, from the above, What is the slope-intercept form of a linear equation? g = 20 2.5 (8) = 0 when we go over here. Hence, We know that, (-10, 2), (-8, 3), (-6, 5), (-8, 8), (-10, 6) How far does light travel in 15 seconds? Each vertical line is intersecting the graph at more than one point. The vertical axis represents the depth, Question 2. 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