Graph each function. state the domain and range f(x)= {-x-2if x>0

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Step-by-step explanation:

For values of x less than zero, the graph of the function is a graph of the line

 y = -x

Because the function is defined by this expression at x=0, there will be a solid dot at the end of the line there, at (0, 0).

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For values of x greater than 0, the graph of the function is a graph of the line

 y = -x -2

This line has the same -1 slope as before, but has a y-intercept of -2. The function is not actually defined as (0, -2), so there is an open circle at the end of the line there.

, 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

step-by-step explanation:

the triangles are similar. therefore the corresponding sides are in proportion:

              cross multiply

            divide both sides by 32