Which function represents the graph of h(x)=2|x-3| + 1 after it is translated 2 units to the right?

Step-by-step explanation:

Translation to the right is given by a positive value of h in the following template:

g(x)=f(x-h)

if we would like to translate to the right by 2 units, h=2, so we replace all the "x" in the definition of f(x) by (x-2).

Here,

h(x)=f(x)=2|x-3|+1

replace x by x-2 gives the translated function

g(x)=f(x-2)=2|x-2 -3|+1 which simplifies to

g(x)=2|x-5|+1

, 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