## Fanduekisses one year ago Graph Transformations: What does a negative sign do to an absolute value graph if it's in front of the || ?

1. Fanduekisses

I know that if it's in fron of the x it flips the graph. What about in this case: $-|-x-3|+2$

2. zepdrix

When the negative is on the x, it flips it horizontally. Example: $$\large\rm f(x)=\sqrt{x}$$ would flip across the y-axis if we did this: $$\large\rm g(x)=\sqrt{-x}$$ A negative played on the outside of everything, is really just a negative being placed on y. And it results in a flip vertically. Example: $$\large\rm j(x)=x^2$$ would flip across the x-axis if we did this: $$\large\rm k(x)=x^2$$ But with your problem, notice that we have neither of these things happening. We're not applying the negative to the 2. So normally I would say, we're reflecting the graph about the x-axis. But in this case, we're reflecting the graph about the line y=2.

3. zepdrix

Woops, $$\large\rm k(x)=-x^2$$

4. Fanduekisses

Ohh so in this case it flips both horizontally and vertically?

5. zepdrix

|dw:1442976962331:dw|The $$\rm \color{green}{green}$$ is the original function. The $$\rm \color{blue}{blue}$$ is the new one. The function is being reflected vertically across the $$\rm \color{#DD4747}{pink}$$ line.