Use interval notation to indicate all real numbers between and including −4 and 7.

[-4,7]

Step-by-step explanation:

square brackets [ ] mean including the number and parenthesis ( ) don't include the number. Also lowest number goes first and biggest number goes second.

[-4, 7]

Step-by-step explanation:

the ‘( )’ implies not inclusive of, whereas ‘[ ]’ implies inclusive of

Therefore, that is the answer,

things to note in general:

- the values should go in ascending order from left to right

e.g (x, x+1) where x is a real number

- if you want to connect two intervals, you would use U or union

e.g (2, 3)U(4,5]

- also, from the previous answer, it is valid if you use set notation such as ‘(x, y]’ and ‘[x, y)’ where x < y, x and y are real

These are equivalent in ‘inequality notation’ as, if we consider p to be in these intervals:

x < p <= y

And

x <= p < y

respectively,

- If we have, say

(x,y]U[y,z) where x, y and z are real, x<y<z

You could combine it to form

(x,z)

Another example would be:

let p be in this domain

[x,x]

Which is equivalent to saying,

x<=p<=x

But by the squeeze theorem, we get that p = x

-notating asymptotes:

for asymptotes that graphs don’t exist beyond it, say, the range of y = e^x

it can be expressed as

(0, inf)

note that infinity is not, as I know of it, considered an asymptote, but we just can’t get to it exactly.

You can define infinity as, paraphrasing here ‘the number of numbers’

we actually can’t assign a value to that, as there will be a number at least 1 greater than any number you specify, but I digress,

The asymptote here is really y = 0 as when x is negative, we can reciprocate to get a fraction, which has 1 in the numerator.

But we all know that a fraction with a constant numerator cannot equal 0 for any denominator in the set of real numbers

Therefore, the asymptote is y = 0

Applying the same logic,

for asymptotes that graphs do exist beyond them, say, y = 1/x

The range is

(-inf, 0)U(0, inf)

where the asymptote is again y = 0

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for