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:
8
x
3
+
2
x
2
−
3
x
+
18
Explanation:
We have:
(
2
x
+
3
)
(
4
x
2
−
5
x
+
6
)
Now let's distribute this piece by piece:
(
2
x
)
(
4
x
2
)
=
8
x
3
(
2
x
)
(
−
5
x
)
=
−
10
x
2
(
2
x
)
(
6
)
=
12
x
(
3
)
(
4
x
2
)
=
12
x
2
(
3
)
(
−
5
x
)
=
−
15
x
(
3
)
(
6
)
=
18
And now we add them all up (I'm going to group terms in the adding):
8
x
3
−
10
x
2
+
12
x
2
+
12
x
−
15
x
+
18
And now simplify:
8
x
3
+
2
x
2
−
3
x
+
18
Step-by-step explanation:
Answer:
everthing is true about it
Step-by-step explanation:
