Answer:
Step-by-step explanation:
To prove that is a multiple of 7.
Proof by induction:
Let n =1. Then we have 8-1 =7 is a multiple of 7
Thus the P(1) is true.
Let us assume that P(n) is true.
= 7l is true for some integer l
To check for P(n+1)
=LHS
=
Thus we find that this is also a multiple of 7.
If true for n, then true for n+1
Hence we find that since true for 1, we have it is true for all natural numbers.
In this question, a piece-wise function is asked to be graphed.
Piece-wise function:
A piece-wise function is a function that has different definitions, depending on the input.
In this question, the function has three different definitions:
For x between -1(inclusive) and 0, y takes a constant value of -1.
For x between 0(inclusive) and 1, y takes a constant value of -2.
For x between 1(inclusive) and 2, y takes a constant value of -3.
Additionally:
At the inclusive points, the interval is circled, and thus, the graphic is given at the end of this answer.
For another example of the graphic of a piece-wise function, you can check brainly.com/question/16855064
