WILL GIVE BRAINLIEST AND 50 POINTS!
1. Find the vertex of the given function.
f(x) = |x + 1| - 7
The vertex is at (_,_)

2. What are the domain and range of the function?
A. domain (-infinity, infinity) range (f(x) greater than equal to -7)
B. domain (-infinity, infinity) range (f(x) greater than equal to 7)
C. domain f(x) greater than equal to 1 range f(x) greater than equal to -7)
D. domain f(x) greater than equal to 1 range (-infinity, infinity)

The vertex is at (-1,-7).

The answer to 2 is A.

Step-by-step explanation:

You want to make the absolute value be |0|, and you make that by assuming a x that is the opposite of the number that accompanies it.

In this case:

Because:

Then:

And, by making the absolute value equal 0 when finding x, you're left with:

The easiest way is to graph, or make a table of values and see where the graph points.

I graphed it for you.

You can clearly see how the vertex, at (-1,-7) is the lowest point, telling you that the range is from that point upwards, or

Then, because you're dealing with absolute values, which never bend and make perfect 90° angles at their vertex, it is safe to assume both lines never touch and continue to opposites ends of the x-axis, or (-infinity, infinity) which is your domain.

1. (-1,-7)

2. A. domain (-infinity, infinity) range (f(x) greater than equal to -7)

Step-by-step explanation:

f(x) = |x + 1| - 7

Has a vertex at:

(-1,-7)

The domain is all real values of x

Range is greater than/equal to -7