Week 3
1. Draw a graph that has 2 values of y for one x, that is.. you can draw a verticle line through 2 points on your graph
2. Is a function.. no 2 different y values for the same x value
3. Your table should include the same x value with different f(x) values
4. t=f(h) or temperature = f(hours of sunshine)
5. Start at (0,0), go to (1,3), (2,0) (3,0) (4,0) (5,0) (6,5) Graph goes through these points. Dist = y, time = x
6. a. Your net profits increase until 1993 when you have a downturn until the last quarter of 1993 and then you start increasing your profits but slow your increase after the start of 1994
7. a. m=-6, b. (0,5), c. f(x) = -6x+5, d. (5/6,0)
8. They are parallel if they have the same slope and no points in common. They are the same line if they are parallel and have a point in common.
9. find the slope: (1,3) and (4,5)… the run is from 1 to 4, or 3. the rise is from 3 to 5, or 2. the slope then, is 2/3. Now find b. To do this, pick one of the point above and substitute i to the equation y = 2/3x + b. You have 2 choices, 3 = 2/3(1) + b or 5 = 2/3(4) + b in either case, if you solve for b you will get b = 2 and 1/3 (subtract 2/3 from both sided, or 8/3 from both sides)
10. Graph goes through (0,3) and has a slope of 2
11. 4
12. y intercept is where the graph crosses the y axis. x intercept is where the line crosses the x axis. To find the y intercept, set x = 0 in the equation y=mx+b. To find the x intercept, set the y = 0 in the same equation and solve for x.
13. Center A graph starts at (0,100) and has a slope of 25 on the graph where x = months and y = dollars spent. The equation, then is y=25x+100. Center B graph starts at (0,50) and has slope 30. Equation B is y = 30x + 50. You can solve this graphically by seeing where they cross, or using substutution. After 10 months you have spent the same at either center. So if you are going to be at the center less than 10 months, use B, If longer than 10 months, use A. If exactly 10 months, it does not matter.
14. -2. Check this on the mathway.com site. Try other examples. Use ()
15. There are 5 even numbers and 5 vowels. There are 5 ways to get an even number as your first number, 5 ways to get an even number for your second number, 10 ways to get the 3rd number (any number will do for this spot), 26 ways to get the 4th digit, or your first letter, only 5 ways to get the 5th digit, since it must be a vowel. and then 26 ways to get the last or 6th digit since it can be any letter. So.. the answer is: 5(5)(10)(26)(5)(26) or 845,000