Answer:
Answers are in bold (in order)
Explanation:
For the table, the question is asking us to take our x value and put it into the equation. for example:
y = 8x +1 . if x = 0, we can write this as this
y = 8(0) + 1 -> (the brackets mean times)
8 x0 = 0. 0+1 = 1.
if we follow this rule, the values are: 1, 9, 17, 25, 33.
For the function machine, if x = 1, then we can write 1 where the x is. The function machine is telling us that 1 x3 and then -2 = y, y being a random number we don't know. 1 x 3 = 3. That means 3-2 = y . 3-2 = y. So, y = 1 when x = 1.
When x =-9 we can rewrite x as -9. That means that -9 x 3, then -2 = y.
-9 x 3 = -27.
That means that -27 -2 = y
-27 -2 = -29, so when x = -9, y = -29.
For the third part we need to work out the gradient and the equation of the table. The gradient (how much our values go up by) The gradient can be worked out by diving the change in y (our y value) by the change in x (our x value). So, if we take the first two y values, we have -2 and 8. The difference/chance between these two is 10. (-2+10=8). And for the x values, the first two x values are 0 and 1. The difference/change between these two is 1. (1-0=1.) So, all we need to do is divide these values 10/1 = 10. So our gradient is 10. That means that the first box on the function machine will be “x10” to work out the second, we simply do the first box and go from there. If our x = 1, then 1 x 10 = 10. Our table says that when x = 1, y = 8. So to we need to work out the change between these is, to get our answer. To get from 10 to 8, we minus two. So the final box on the function machine must be “-2”
For the last part of the question, we are just substituting in the values of x.
If t = 1, then 4(t-3) is basically 4(1-3)
1-3 = -2. 4(-2) = -8.
so when t =1, s = -8. If you do this for the next two questions, you should get the answers:
s = -28 when t = -4
s = -12 when t = 0