Math /7 NTES (9.3) Name Graphing Linear Functions The collection of all input values is called the of a function. The collection of all output values is called the of a function. Make a table for the function. Identif the range of the function. 1. f() = Domain: 0, 1,, 3. = + Domain: 11, 15,, 7 3. = 3 Domain: 5, 9, 1, 19 f() = f() = + f() = 3 Range: Range: Range:. You have a bo with 7 plants that ou are planting in a garden. Write a rule for as the function of, where is the number of plants ou have left in the bo; is the number of plants ou have put in the garden so far. a) In the beginning =, =. b) Each time ou put one plant in the garden, ou have one less plant in the bo, so = f() = c) Make a table and build the graph f() (, ) d) Domain Range e) What are the coordinates of the point of intersection of the graph and the -ais? What does -intercept represent? f) What does the point P represent? g) What are the coordinates of the point of intersection of the graph and the -ais? What does -intercept represent?
Find each function value. 5. f() if f() = +. f(9) if f() = 7. f(3) if f() = + Complete the function table. Then graph the function.. 9. -int: -int: -int: ; -int: ; Identif the -intercept and the -intercept of the graph. 10. 11. 1. -int: ; -int: -int: ; -int: -int: ; -int: Graph each function. 13. 1. 15.
Math /7 Practice (9.3) Questions 1. Determine whether the relation is a function. Eplain. 1.. 3.. 3 5 5 10 7 5 9 5. {(5, 9), (, ), ( 7, ), (0, ), (, ), (3, 9), ( 3, )}. {(3, 9), (, ), ( 7, ), (0, ), (, ), (3, 5), ( 3, )} Questions 7-, Use the chart to answers. Determine whether the relation is a function. Eplain. 7. Describe how the area of a square is related to the length of the side. a. As the length of the side increases, the area decreases. b. As the length of the side increases, the area increases and then decreases. c. As the length of the side increases, the area increases. d. As the length of the side increases, the area decreases and then increases.. Is the relation (side length, area) a function? Eplain. a. No, there is a side length with areas paired with it. b. No, there are no negative area values. c. No, one side length is equal to the area value. d. Yes, each side length is paired with onl one value for the area. Area of a Square Side Length Area (cm ) (cm) 1 1 3 9 1 5 5 Which set of ordered pairs are solutions to the following function? 9. = -3 a. b. c. d.
Math /7 Homework (9.3) Identif the -intercept and the -intercept of the graph. 1.. 3. -int: ; -int: -int: ; -int: -int: ; -int:. The table shows the apparent temperature P F, as it feels to our bod, as a function of the real air temperature A F when there is 10% humidit. Graph the function. Air temperature ( F), A 70 75 0 5 90 95 Apparent temperature ( F), P 5 70 75 0 5 90 Rule of the function: P = Find each function value. 5. f() if f() = +. f(9) if f() = 7. f(3) if f() = + f() = f(9) = f(3) = Graph each function.. f() = 9. f() = 3 10. f() = (,f()) 3 (,f()) f()
Math /7 Enrichment (9.3) A function flowchart and ten numbers are given below. Input each number into the flowchart at the place marked START, then follow the number through the flowchart. When ou reach the place marked STP, record the output number.
- NAME DATE PERID Stud Guide and Intervention Linear Equations in Two Variables A function can be represented with an equation. An equation such as 1.50 is called a linear equation. A linear equation in two variables is an equation in which the variables appear in separate terms and neither variable contains an eponent other than 1. Linear Equations 1,, 1 3 Nonlinear Equations 1, 3, 3, Solutions of a linear equation are ordered pairs that make the equation true. ne wa to find solutions is to make a table. Eample 1 Eample Complete the table. Use the results to write four solutions of 10. Write the solution as ordered pairs. 10 (, ) 1 ( 1) 10 1 ( 1, 1) 0 (0) 10 10 (0, 10) 1 (1) 10 (1, ) () 10 (, ) A linear equation can also be represented b a graph. The coordinates of all points on a line are solutions to the equation. Graph 10 b plotting ordered pairs. Plot the points found in Eample 1. Connect the points using a straight line. (, ) (1, ) 10 (0, 10) 1 1 Eercises Find four solutions of each equation. Write the solutions as ordered pairs. 1 3. Sample answers are given. 1.. 3 7 3. 5 ( 1, ), (0, ), ( 1, ), (0, 7), ( 1, 9), (0, 5), (1, ), (, ) (1, 10), (, 13) (1, 1), (, 3) Graph each equation b plotting ordered pairs.. 5.. 1 1 1 1 1 11 Glencoe/McGraw-Hill Glencoe Pre-Algebra
- NAME DATE PERID Practice Linear Equations in Two Variables Find four solutions of each equation. Write the solutions as ordered pairs. 1. Sample answers are given. 1. 5. 7 3. 3 1 ( 1, ), (0, 5), ( 1, 7), (0, 7), ( 1, ), (0, 1), (1, ), (, 3) (1, 7), (, 7) (1, ), (, 5). 5.. 7 1 ( 1, 7), (0, ), ( 1, ), (0, ), ( 1, 1), (0, 1), (1, 5), (, ) (1, ), (, ) (1, 7), (, 0) Graph each equation b plotting ordered pairs. 7. 1. 9. 1 10 + + 10. 7 11. 3 9 1. 1 10 7 10 3 9 1 CKING For Eercises 13 15, use the following information. Kirsten is making gingerbread cookies using her grandmother s recipe and needs to convert grams to ounces. The equation 0.0 describes the approimate number of ounces in grams. 13. Find three ordered pairs of values that satisf this equation. Sample answer: (100, ), (00, ), (300, 1) 1. Draw the graph that contains these points. 15. Do negative values of make sense in this case? Eplain. No; a recipe cannot contain a negative number of grams of an ingredient. Glencoe/McGraw-Hill Glencoe Pre-Algebra unces 7 5 3 1 100 00 300 00 Grams
- NAME DATE PERID Enrichment Equations with Two Variables Complete the table for each equation. 1. 7. 3. 9 3 5 1 1 1 1 3 5 0 9. 3 5.. 1 1 5 3 7 1 1 5 11 13 7. 9. 9. 3 5 5 3 3 1 7 1 3 7 1 9 10 10 10. 11. 3 1. 1 1 1 1 3 5 0 3 1 3 3 7 5 11 Glencoe/McGraw-Hill Glencoe Pre-Algebra
-3 NAME DATE PERID Stud Guide and Intervention Graphing Linear Equations Using Intercepts Finding Intercepts The -intercept is the -coordinate of a point where a graph crosses the -ais. The -coordinate of this point is 0. The -intercept is the -coordinate of a point where a graph crosses the -ais. The -coordinate of this point is 0. To find the -intercept, let 0 in the equation and solve for. To find the -intercept, let 0 in the equation and solve for. Eample 1 Find the -intercept and the -intercept for the graph of 5 10. To find the -intercept, let 0. 5 10 Write the equation. 5(0) 10 Replace with 0. 5 Simplif. To find the -intercept, let 0. 5 10 Write the equation. Eample (0, ) 5 10 (5, 0) Graph 5 10. (0) 5 10 Replace with 0. Simplif. Eercises Find the -intercept and the -intercept for the graph of each equation. 1. 5. 1 0 3. 3 1 5; 5 none; 1 ; Graph each equation using the - and -intercepts. Lesson -3. 3 3 5. 5. 9 ( 1, 0) (0, 3) 1 9 1 9 3 3 3 9 1 (0, 9) 3 (9, 0) 9 1 ( 5, 0) (0, 5) Glencoe/McGraw-Hill 7 Glencoe Pre-Algebra
-3 NAME DATE PERID Skills Practice Graphing Linear Equations Using Intercepts State the -intercept and the -intercept of each line. 1.. 3. 10 3; none; ; Find the -intercept and the -intercept for the graph of each equation.. 5. 3 5 30. 9; 1 10; ; 7. 7 1. 1 9. 7 ; 1 1 ; none; 7 Graph each equation using the - and -intercepts. 10. 11. 1. (0, ) + (3, 0) (0, ) (0, ) + ( 1, 0) 13. 1. 15. 3 5 (0, 3) 3 (0, ) (5, 0) 5 (, 0) (3, 0) Glencoe/McGraw-Hill Glencoe Pre-Algebra
-3 NAME DATE PERID Practice Graphing Linear Equations Using Intercepts Find the -intercept and the -intercept for the graph of each equation. 1.. 0 3. 3 9 1, none, 3, 9. 1 5. 5 3 15. 7 0, 3, 5 7, none Graph each equation using the - and -intercepts. 7. 7. 5 9. 7 (7, 0) (0, 7) (0, 5) + 5 (5, 0) (0, ) (, 0) 10. 1 1 11. 5 10 1. 7 ( 7, 0) (0, 1) 1 1 7 5 + 5 (0, 5) (, 0) (, 0) Lesson -3 13. SAVINGS Rashid s grandparents started a savings account for him, contributing $1000. He deposits $30 each month into the account. The equation 30 1000 represents how much mone is in the savings account after number of months. Graph the equation and eplain what the -intercept means. The -intercept 1000 shows how much mone was in the savings account before Rashid made an deposits. $ (thousand) 1 1 1 1 10 30 1000 5 10 15 0 Months Glencoe/McGraw-Hill 9 Glencoe Pre-Algebra