The graph of f(x) = |x| is translated 6 units to the right and two units up from a new function. which statement about the range of both function is true?

DOMAIN: All Real Numbers   OR   (-∞,∞)

RANGE: y ≥ 2   or    [2,∞)

Step-by-step explanation:

The original function f(x) = |x| has a v-shape and the vertex (tip) is at (0,0).

The domain of f(x) = |x| is all real numbers.  Shifting it to the right is not going to change the domain.

The range of f(x) = |x| is y ≥ 0 because the "V" opens upward and starts at zero.  Moving the function up two units will move the vertex up by 2 so the function now starts at y=2 and goes up, so the range is y ≥ 2.

answer: about 22.67

step-by-step explanation:

, 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