2 SPI 0706.3.2, .3.3, .3.5, .3.7 Essential Questions: How can I tell if a relation is a function?How do I make tables and write equations for functions?How do I graph data to show relations or functions?
3 Essential Question: How do I make a function table for a relation (equation)? 1. Complete the function table for y=6-x Use the keep, change, change rule when subtracting -4 from 6. Check your work by plugging in the numbers: 10=6- -4 or 10=6+4.XFunction rule y= 6-xy-4Y=6- -410-22
4 Essential Question: What is the domain of a relation or set of ordered pairs? 2. What is the domain for the function in #1? Hint: domain is the same as all numerals under X.xFunction rule y= 6-xy-4Y=6- -410-22
5 Essential Question: How do I graph a function? Graph the function y=4x + 1First make a table:x4x + 1y4 (0) +1123
6 #3 continuedNow graph the data in the table. The first point on the graph has been done for you. Connect the points.1412111098765432.1-1-2-3
7 Essential Question: How do I find the slope of the line that passes through two points on a graph? 4. Find the slope of the line that passes through the points A (2, -1) and B (5,2). Y2-Y1/ X2 – X1 = Slope 2- -1/5- 2 = Don’t forget to use the “keep, change, change” rule because you are subtracting positive and negative integers .
8 Essential Question: How do I graph data on a table to show functions? 5. Fundraising Laurel is selling plants for a fundraiser. The table shows how the number of plants she sells is related to the amount of prize money she receives. Graph the function.Num-ber of Plants Sold255075100150200Prize Money$510152030
9 #5 continued Prize 40 Money 35 In 30 $ 25 20 15 10 5 50 100 150 200 50100150200Number of Plants Sold
10 Essential Question: How can I use a graph to make predictions? 6. Use the graph in #5 to determine how many plants Laurel sells if she receives $35 in prize money. Hint: If Laurel sells 125 plants she will receive $25 in prize money. I can tell by looking at the line I have drawn to connect the points. First I look at where 125 is on the bottom, then move my eyes or finger up to the line. Look across to the y axis and locate where the prize money is at $25.
11 Essential Question: How do I find the rate of change from a table? Find the rate of change from the table.Change in temp. is +4 each time; change in time is +2 each time. 4/2 =TimeTemperature230434638
12 Essential Question: How do I use a graph to find the rate of change? 8. Use the graph on your worksheet (it is more accurate than my graph) to find the rate of change. Hint: Rise/Run; make ordered pairs out of each point on the graph (starting with 2/1); reduce the ratios of rise/run to find the rate of change.Meat10(lbs)8642135Number ofPeople
13 Essential Question: How do I write equations to show relationships? 9. And 10. Phones Rosemary earns $8 per hour working part-time at an animal hospital. Write an equation to show the relationship between her total earnings y for x hours worked. Y = _____x 10. How much will she earn in a month if she works a total of 22 hours? Y= _____ times 22.
14 Essential Question: How do I graph data from a table? 11. Television Graph the data using the graph on your study guide.AgeHours of TV Watched per week51511251735234529
15 Essential Question: How do I use a graph to estimate an answer? 12. Use the graph in #11 to estimate the number of hours of television watched by someone 30 years old. Hint: After you connect the points on your graph, look at the bottom of the graph on the line between 25 and 35 years. Look up from there to your line, then across to the hours. What number is it close to?
16 Essential Question: How do I determine the function from a function table? P. 61, Form 2A1. Which function matches the function table at the right?Hint: find the slope by using y2-y1/x2-x1; find the 2 selections that have the same number next to the x (also called slope). Plug in the numbers in the table to find the correct one.XY-3-14-2310
17 Essential Questions: What is the domain? What is direct variation? 2. What is the domain of the function shown in #1? Hint: the domain is the set of x’s.3. If y varies directly with x and y = 7 when x= -14, what is y when x= 3?y/x= y/x7/-14= y/3-1/2= y/3-1/2 (3)= y/3 (3)Y=
18 Essential Questions: How do I find slope from 2 points on a line Essential Questions: How do I find slope from 2 points on a line? How do I find ordered pairs on a graph from a function rule? How do I graph a function?4. What is the slope of the line that passes through the points A(0,3) and B(2,0)? Y2-y1/x2-x1= 0-3/2-0= 5. Which ordered pair is not a point on the graph of y= -x + 5? Plug the numbers in each of the options with the first number in each ordered pair as X, the second is Y. 6. Which function is graphed on your study guide? If it is a positive line direction, eliminate the negative line direction options; If it is a negative line direction, eliminate the positive line direction options. Count from -2 y intercept on the graph; how many lines does it rise and how many does it run before it intercepts with the x axis? Y/x is rise/ run.
19 Essential Questions: How do I determine the line on a graph from a function rule? How do I calculate slope from a line on a graph?7. Which line is the graph of y=x-2? There is only one line that has -2 as the y intercept. 8. What is the slope of line l in the graph for #7? Slope is rise/run; one point on the line is rise 3/run 1or 3/1; line is negative because of the direction. So what is the answer?