We want to see which graph represents the given function.
Sadly we don't have the options so I will post the correct graph at the end of the answer.
Here our function is:
f(x) = |x + 2| + 1
This is a transformation on the parent absolute value function, that as you may know is a conformed of two lines:
y = x
y = -x
The first one for positive values of x and the second one for the negative values of x.
Now, remember the general translations
Horizontal translation:
For a general function f(x) a horizontal translation of N units is written as:
g(x) = f(x +N)
If N is positive the translation is to the left, if N is negative the translation is to the right.
Vertical translation:
For a general function f(x) a vertical translation of N units is written as:
g(x) = f(x) + N.
If N is positive the translation is upwards and if N is negative the translation is downwards.
Now that we know that, we can see that our function:
f(x) = |x + 2| + 1
Will have a graph equal to the one of the parent function, but moved 2 units to the left and one unit upwards.
The graph can be seen below:
If you want to learn more, you can read:
https://brainly.com/question/24401156
