Answer:
Explanation:
To tackle this problem, you start with the simplest function y = |x| (the absolute value of x). This is a function that turns any negative number into a positive number while positive numbers stay positive.
For example, if x = -1, you would get y = 1.
Or if you have a x = -10, you would get y = 10.
Now let's say you have a positive number x = 5, then you'd also get a positive number y = 5.
That's why the graph of y = |x| is a V shaped graph that has the vertex at (0,0) which opens upwards. (see the attached photo1)
Now let's find out what happens when we change the function of y = |x| into y = |x+1|.
What happens is that the graph of the old function gets shifted 1 unit to the left. Thus the new vertex will be moved to (-1,0). (see the attached photo2)
Now let's see what happens when we put a negative sign to the function so it becomes y = -|x+1|.
Putting a negative sign on front of the function is equivalent by multiplying the function by -1 which makes your old positive y values turn into negative y values. That is why you'll see the new graph to be flipped (reflected) via the x-axis. Which means the V will now open downwards. (see the attached photo3)
Now let's find out what happens when we subtract 5 to the function so it becomes y = -|x+1| - 5.
Subtracting 5 to the function shifts the graph 5 units downwards. Hence the new vertex will now be placed at (-1,-5). (see the attached photo4)
Therefore the answer is the 4th choice which is:
a V shaped graph with vertex at (-1,-5), which points down.
- Ginno Pineda