In piecewise linear functions, the endpoint of one segment and the initial point of the next segment can have the same x-coordinate but a different value of f(x).
Such difference in values is called a step or discontinuity and such a function is called a discontinuous function.
Here in this case, there are 3 discontinuities: x=-3, x=3 and x = 5.
x = -3 because x is smaller than or greater than -3 but not equal.
x = 3 since greater than 3 in one of the inequalities.
x = 5 since x is smaller than 5 in one of the limits.
Answer:
The graph is the 4th picture
Step-by-step explanation:
When graphing, you take the opposite if there is a number in the absolute value bars. If there is, then you will be going towards the x axis. If there is a number outside of the absolute value bars, assume that this will be the y axis
Answer:
See below.
Step-by-step explanation:
First, notice that this is a composition of functions. For instance, let's let 
and 
. Then, the given equation is essentially 
. Thus, we can use the chain rule.
Recall the chain rule: ![\frac{d}{dx}[f(g(x))]=f'(g(x))\cdot g'(x)](https://tex.z-dn.net/?f=%5Cfrac%7Bd%7D%7Bdx%7D%5Bf%28g%28x%29%29%5D%3Df%27%28g%28x%29%29%5Ccdot%20g%27%28x%29)
. So, let's find the derivative of each function:
We can use the Power Rule here:
Now:
Again, use the Power Rule and Sum Rule
Now, we can put them together:
Answer:
1st Blank: 5
2nd Blank: 3
3rd Blank: -8
4th Blank: -8
5th Blank: 12
Step-by-step explanation:
15x+35y=-100
-15x+9y=-252
___________
44y=-352
___ ___
44 44
y=-8
3x+7(-8)=-20
3x-56=-20
+56 +56
__________
3x=36
__ __
3 3
x=12
