A relation is (also) a function if every input x is mapped to a unique output y.
In terms of graphical representation, this implies that a graph represents a function if there doesn't exist a vertical line that intersects the graph more than once. So:
- The first graph is exactly a vertical line, so it's not a function.
- The second graph represents the function y=x, so it's a function: you can see that every possible vertical line crosses the graph only once.
- The third graph is not a function, because you can draw vertical lines that cross the graph twice.
- Similarly, in the fourth graph you can draw vertical lines that cross the graph twice
- The fifth graph is a function, because every vertical line crosses the graph once
- The last graph is a function, although discontinuous, for the same reason.
Answer:
and 
Step-by-step explanation:
Given that 
and 
, the parametric equations are obtained by algebraic means:
1) Given
2) 
Given
3) 
Associative and modulative properties
4) ![y = 5\cdot \left[(-1)^{-1} \cdot (-1)\right]\cdot x +11](https://tex.z-dn.net/?f=y%20%3D%205%5Ccdot%20%5Cleft%5B%28-1%29%5E%7B-1%7D%20%5Ccdot%20%28-1%29%5Cright%5D%5Ccdot%20x%20%2B11)
Existence of multiplicative inverse/Commutative property
5) ![y = [5\cdot (-1)^{-1}]\cdot [(-1)\cdot x]+11](https://tex.z-dn.net/?f=y%20%3D%20%5B5%5Ccdot%20%28-1%29%5E%7B-1%7D%5D%5Ccdot%20%5B%28-1%29%5Ccdot%20x%5D%2B11)
Associative property
6) 
/ 
7) 
Modulative property
8) ![y = -5\cdot [-x + 2 + (-2)]+11](https://tex.z-dn.net/?f=y%20%3D%20-5%5Ccdot%20%5B-x%20%2B%202%20%2B%20%28-2%29%5D%2B11)
Existence of additive inverse
9) ![y = -5 \cdot [(2-x)+(-2)]+11](https://tex.z-dn.net/?f=y%20%3D%20-5%20%5Ccdot%20%5B%282-x%29%2B%28-2%29%5D%2B11)
Associative and commutative properties
10) 
Distributive property
11) 
12) 
By 1)
13) 
/Result
14) 
Compatibility with addition
15) 
Compatibility with addition
16) ![[t+(-t)]+x= 2 + [x+(-x)]+(-t)](https://tex.z-dn.net/?f=%5Bt%2B%28-t%29%5D%2Bx%3D%202%20%2B%20%5Bx%2B%28-x%29%5D%2B%28-t%29)
Associative property
17) 
Associative property
18) Associative and commutative properties/Definition of subtraction/Result
In consequence, the right answer is and .
Step 2: it should be P-2x, not +.
Hope this helped :)
Answer:
complementary angles
Step-by-step explanation:
The sum of the angles is 67+23 = 90
When angles sum together to 90, the are called complementary
Answer:
B)
Step-by-step explanation:
