What is the domain of the function graphed below?

x < 7

Step-by-step explanation:

the domain is the number range or interval of x the function is defined for to generate a y-value.

the graph shows that the y-values continue with x-values to the right up to but not including 7 (the empty dot says "excluding"). and with x- values to the left to negative infinity.

x=-1 is not a problem, because while for the left part of the function it is not included, but for the right part it is.

so, it is fully defined for all x < 7.

, 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

you can use a^2+ b^2=c^2