Which graph represents the function f(x)=|x+2|+1

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:

link

The graph in the attached figure

Step-by-step explanation:

we have

Using a graphing tool

The graph is a "V" shape

The vertex is the point

The y-intercept is the point

see the attached figure

the 2 figures are congruent bc if you reflect abcd over the y axis then over the d axis the figures overlap