Question

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

Answer 1

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

Answer 2

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.

Answer 3

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

Answer 4

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

Answer 5

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.