college algebra

Question

Write the function that shifts f(x)=x^2 three units right and 1 unit down.

Answer 1

August,

If the lowest point is (0,0) what should happen for the graph to go dawn 1 unit? Would you add or subtract a constant? By adding/or subtracting a constant at the "finish" you only change the final y value (i.e. up or dawn).

Now You have f(x) -1. That is x²-1. 

Now think of moving the point (0,0) to the right to where x=3 is. In order for your y value to stay the same "0" what has to happen to the x value? Some thing has to be done to 3 to get it to become "0." That something is subtracting 3 form it. That is f(x-3).

(x-3)²-1

 

Answer 2

Hello, thank you for taking the time to post your question!

For the horizontal shift, you modify the x variable inside the function, so that means replacing “x” with (x – 3).

Then for the vertical shift, you add/subtract outside of the function, so that means subtracting by 1 on this one

Putting it all together then the function

f(x) = x^2 becomes

g(x) = (x – 3)^2 – 1

I hope that helps you get moving in a better direction on this type of question! Feel free to reach out if you have any additional questions beyond that :)