Star with the statement: "Given that the sum is 11"
which may seem a bit odd considering its the last part of the problem
The "given" is important as it sets up the constraints of what we're dealing with. In this case, we know 100% (we can see or someone told us without lying) that the sum is 11. We don't know what the individual values are but we know they add to 11.
What are the ways to add to 11? Well they are...
5+6 = 11
6+5 = 11
so there are 2 ways to do it. As you can see, none of those ways involve a double. A double is where we have two of the same values (eg: snake eyes which is 1 and 1 giving 1+1 = 2 as the sum). It turns out that it's impossible to have doubles add to any odd number.
So if we know the sum is 11, and we're asking "what is the probability of rolling doubles", then the answer is 0.
The 0 indicates "impossible" or "certainty of it never happening".
Answer:
When we have a function f(x), the values of x at which the function is not differentiable are:
1) values at which the function is not "soft". So if we have a really abrupt change in the curvature of the function, we can not differentiate in that value of x, because in those abrupt changes there are a lot of tangent lines to them.
One example of this is the peak we can see at x = -4
Then we can not differentiate the function at x = -4
2) When we have a discontinuity.
If we have a discontinuity at x = x0, then we will have two possible tangents at x = x0, this means taht we can not differentiate at x = x0, and remember that a discontinuity at x = x0 means that:
f(x0₊) ≠ f(x0₋)
where x0₊ is a value that approaches x0 from above, and x0₋ is a value that approaches x0 from below.
With this in mind, we can see in the graph a discontinuity at x = 0, so we can not differentiate the function at x = 0.
Answer:
g(x) = 1/3 (x - 12) .. vertical compression with factor 1/3 from f(x-4)
Step-by-step explanation:
*f(x) = x - 8 ... horizontal translation right 8 units from parent function f(x)=x
f(x-4) = (x-4) - 8 = x - 12 .... horizontal translation right 4 units from f(x)=x-8
g(x) = 1/3 (x - 12) .. vertical compression with factor 1/3 from f(x-4)
