Question

1. Describe how the graphs of y=|x| and y=|x|-15 are related.
2. Graph y=|x|-2.
3. Graph y=-|x-4|.
4. Write an equation for the translation of y=|x|, 2 units down.
5. Graph the equation by translating y=|x|, y=|x+7|

Answer 1

#1,2,4: translation up or down is done by adding or subtracting from y.
If y = f(x)
then y = f(x) +3 shifts the graph up.

#3: reflection through the x-axis is done by changing the sign of y. What was above goes below, etc.
y = -f(x) reflects f(x) through the x-axis.

#5: replacing x with (x-h) shifts the graph to the right.
replacing x by (x+h) shifts to the left by h.

There are lots of good online graphing sites.
desmos and wolframalpha come to mind.
Enter your functions and see what happens.

Answer 2

I use mathway for quick checks after brainly and jiskha... Just saying