Question

How do you identify the transformation of `h(x)=-2sqrt(x-4)`?

Answer 1

Let's look at the parent function, `y = sqrtx`

graph{y = sqrtx}

Now let's shift it to the right by `4` to give us `y = sqrt (x-4)`

graph{y = sqrt(x-4}

Now we can stretch the graph by a factor of `2` by multiplying the equation by `2`: `y = 2sqrt(x-4)`

graph{y = 2sqrt(x-4)}

And now we deal with the negative sign. This flips the graph across the `x`-axis

graph{y=-2sqrt(x-4)}

There we go! We took the parent graph, `sqrt(x)` and shifted it to the right `4` units, then we stretched the graph by a factor of `2`, and finally we flipped the graph across the `x`-axis.