If anyone could help i'd really appreciate it
Describe how y= f(x) is transformed by each of the following:
a) y= -f(x+2) - 5
b) y= f(-x) + 5
Any good algebra textbook should have a table summarizing function transformations. Here's a table that I got from this website:
I'll help you get started. If you have , identify the things that are going on. For instance, there's a negative sign in front of the f(x). According to the table, that's a reflection of the function about the x-axis. Continue that methodology for +2 inside the function notation, and the -5 outside of the function notation.
on top of what semouey161 said, when given questions where you have to APPLY transformations to functions, it's important to do them in a certain order (stretches/compressions first, then reflection (which is basically a special type of stretch), and then translations).
For the questions that you posted above, it helps to remember that some of the "modifiers" on f(x) must be interpreted in an in unintuitive way. By that I mean the +2 in part A might make you think +2 to the right since we tend to associate positive with right, but actually +2 means to move 2 to the left. -5 means to move 5 down, but to keep yourself from mixing up which direction of translations should be intuitive/unintuitive, add +5 to both sides so:
y+5 = -f(x+2), then you can use the "unintuitive trick" to determine the direction of the transformations (notice how the vertical translation +5 goes with the y, and the vertical axis is the y-axis. similarly the horizontal translation +2 goes with the x, and the x-axis is the horizontal axis).
Don't worry about the minus sign messing this up.
y+5 = -f(x+2)
-y-5 = f(x+2)
-y = f(x+2) +5
y = -f(x+2) - 5
Rearranging the variables and multiplying both sides by -1 doesn't change the equation and the transformations