Question

Give an example of each of the following
A function whose domain is [2,oo)
An arithmetic sequence
A system of equations with no solutions

Answer 1

y = sqrt(x - 2)
You cannot take the square root of a negative number.
Therefore, x - 2 >= 0 which implies x >= 2
So the domain of the function is: [2, infinity)

Answer 2

Arithmetic sequence is formed by starting with a number and adding some number to get the next number, add the same number and get the next number and so on.
For example:
First number in the sequence: 1
Add the same number, say, 3 to get the subsequent numbers to the series:
1st term: 1
2nd term: 1 + 3 = 4
3rd term: 4 + 3 = 7
4th term: 7 + 3 = 10
5th term: 10 + 3 = 13
...
So the arithmetic sequence is:
1, 4, 7, 10, 13, ........

Answer 3

If, for example, we have two lines that are parallel, they will never intersect and therefore there won't be any common point that satisfies both equations.
Parallel lines have the same slope:
y = 2x + 1 and y = 2x + 5 are equations of two parallel lines that never intersect.
y=2x+1 can be rewritten as:
2x - y + 1 = 0
And the other lines can be rewritten as: 2x - y + 5 = 0
Therefore,
2x - y + 1 = 0 and
2x - y + 5 = 0
are a system of two equations that don't have a solution.

Answer 4

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