Please help me with this multiple transformation of a function problem

[modonnell121]

[h=1][/h] Okay so our teacher gave us this graph of a function f(x), and told us to graph the function transformed into -f(x+2)-1. To obtain my answer I first shifted it to the left 2 units, then I reflected it along the x-axis, then I shifted the function 1 unit down the y-axis. My teacher's answer was different, and was reached by first shifting the function to the left 2 units, then shifting it down 1, and THEN reflecting along the x-axis.

This gives two different graphs. So whose order was correct, and how do I know in the future the order to transform? Please answer if you're knowledgeable because this is very important to me.

 

[Deleted member 4993]

Okay so our teacher gave us this graph of a function f(x), and told us to graph the function transformed into -f(x+2)-1. To obtain my answer I first shifted it to the left 2 units, then I reflected it along the x-axis, then I shifted the function 1 unit down the y-axis. My teacher's answer was different, and was reached by first shifting the function to the left 2 units, then shifting it down 1, and THEN reflecting along the x-axis.

This gives two different graphs. So whose order was correct, and how do I know in the future the order to transform? Please answer if you're knowledgeable because this is very important to me.

As you describe it and I understand it - your answer is correct.

Your teacher was trying to solve the problem following way

y = - f(x+2) - 1 ← y = -[f(x+2) + 1]

y = f(x) + 1 ← implies graph should be shifted up by 1.

so your teacher should have moved the graph up by 1 - then reflect it across x-axis.

Then your answers would be identical.

 

[modonnell121]

thank you for answering and telling me i'm right. here's an image of the actual problem i'm talking about. the graph ends immediately where it ends in the image, which means that my answer doesn't even fit on the provided graph. WTF???

btw the sketched function to the left and below the printed, dark one is my answer except it should (if I'm right) be shifted down one unit. I'm unable to though because the graph ends, as I said.