Answers:
1. A function is a relationship where every input value has at most 1 output value
2. Not a function since there are 2 output values when x=2
3. In your table, make sure every x value has only 1 value for f(x)
4. A function is a solvable problem. If you have 2 output values for a function, which one is the correct one? A fuction is how we will transform equations to solve them.
5. Make sure your graph passes the vertical line test
6. t = f(h) or temperature = f(hour of the day)
7. the logical hottest and coldest temperature you could expect for April 15.. maybe 30 degrees to 70 degrees.. or something close. 20 - 90 degrees if you want to be careful
8. 24.. there are 24 hours in the day. THe domain is the x axis
9. Start when x=0, y=2000000 (don’t mess with drawing this to scale.. rough it in). Your graph would go to (1,1000000) since after 1 year you only have 1 million left. Your next point is at (3,0), since you are broke in year three. Your next point is at (6,0) representing the 3 years you are broke. Lastly you go to (7,30000)
10 The slope is -2/3 since the x goes from 1 to 4 (3) and the y goes from 5 to 3 (-2). Slope = rise over run, or -2/3. Now you have y = -2/3x + b You now have to solve for b. Pick one of your 2 points, it does not matter which. Let’s pick the first one, (1,5). Plug 1 in for the x and 5 in for the y. You now have 5 = -2/3(1) + b. Solve for b by adding 2/3 to both sides. You have 5 + 2/3 = -2/3 + 2/3 + b Or b = 5 and 2/3. Your equation is y = -2/3 x + 5 and 2/3
11. Plot (0, -1), the y intercept since b = -1. Now since the slope is 1/3, to over 3 and up 1. Your next point, then is (3,0). Connect these 2 points and you have your line.
12. Find the average rate of chance between 2 points by taking the difference between the 2 y values and dividing that by the difference between the 2 x values. Rise over run.
13. b = 1, since that is the y intercept. (0,1), then, is on the graph. Now find the slope between (0,1) and (4,5)… run is 4 (0 to 4). The rise is also 4 (1 to 5). So the slope is 4/4 or 1. Therefore, the equation is y = 1(x) + 1 or y = x + 1
14. Plug this into the calculator at mathway.com. Cut and paste.
15. 10 ways to get the first number. 10 ways to get the second number, 26 ways to get the first letter, 26 ways to get the 2nd letter, 26 for the third and 26 for the fourth. Therefore, there are 10(10)(26)(26)(26)(26) different license plates using this format.
16. the first number must be a 2 or 4, so there are 2 possibilities for that. The second number can be anything, so there are 10 possibilities for that one. The first letter must be a vowel, so there are 5 possibilities for the first letter. The second and third letter can be anything, so there are 26 options for the second letter and 26 for the third letter. The last letter must be a vowel, so there are 5 possibilities for that one. Multiply them all together and you get: (2)(10)(5)(26)(26)(5) different licenses you can make that satisfy the given pattern.