1. What you do is replace the x with the x in the order pair and have it equal to y in the order pair. I'll show you.
A) Is correct. 9 = 2^3 + 1, 9 = 8 + 1, 9 = 9.
B) Isn't correct. -3 = 2^-2 + 1, -3 = 1/4 + 1, -3 = 1 1/4.
C) Is correct. 3 = 2^1 + 1, 3 = 2 + 1, 3 = 3.
D) Is correct. 33 = 2^5 + 1, 33 = 32 + 1, 33 = 33.
2. I know that a negative exponent would divide instead of multiply the number so if the number is already a fraction then a negative exponent would make it a whole number. So by knowing that alone you get rid of already A and D.
C) I'll do -2 has the exponent because it has an whole number as the output.
1/2^-2 = 1/2^-2 = 2^2/1 = 4/1. Which is what they showed on the graph for C, but for B they didn't so B can't be correct.
3. It's "As x decreases without bound, f(x) approaches the line y = 3. Because x will keep getting into a smaller and smaller fraction trying to reach for 3 but never ever touching it so it'll be like that for infinity.
4. X is the number years and y is the amount in the bank account. It couldn't be (210,0) because in 210 years if exponential you can't get $0. The horizontal axis is labeled Years is correct. The sketch is drawn in one quadrant because the amount of money and years can only be positive in this case. The horizontal axis is labled Account balance is incorrect because x is the independent varible, and the Account balance is dependent on the years. The vertical axis is labeled Years is incorrect as proven before. The vertical axis is labeled Account balance is correct as proven before.
5. A parent function is the simpliest function in this case 2^x. What the exponential function adds to the function is 5 which is positive so it'll be "Right 5"
6. It's plus one because it'll always be to get to one, just like in problem 3. So the one you'll choose is g(x) = (1/2)^x + 1
7. You can either put both in function form or table, but I'm going to just figure out what the termites is in its current form as a function and then just subtract the two. Termites: f(4) = 4(3)^4 = 4(81) = 324, and for ants on the table it shows 531. 531 - 324 = 189. 189 is the positive difference in the fourth month between the termites and the ants.
8. The point (0,0) doesn't contain the x - intercept because y isn't 0 at that time and will never be 0. The asymptote indicates that there could never be fewer than 0 termites in the colony is correct. The asymptote indicates that there will never be more than 20 termites in the colony is incorrect. The y-intercept represents the number of temites originally in the colony is correct. The line y = 0 is an asymtote of the graph is correct. The point (0,25) contains the y - intercept is correct. The line x = 20 is an asymptote in the graph is incorrect.
9. It's exponential because when I graphed the order pairs and drew one line to connect them it was curved.
10. I used (0,1/16) and (3,4). 4 / 1/16 = 4 x 16/ 1 = 64. I did what they asked and I don't know what to do with 64 as a ratio anyway. Sorry I just don't get this one.
Hope this helps :)
