Question

Graph the original function by indicating how the more basic function has been shifted, reflected, stretched, or compressed.

Answer 1

@extrinix @vocaloid

Answer 2

Okay so you understand that the quadratic equation looks like this
\(f(x)=\sqrt{x-h}+k\)
With \(h\) being the opposite of it's seen value, and \(k\) being it's seen value

In this equation it shows this
\(s(x)=-\sqrt{x+4}-5\)

So, you can see that \(h\) is \(4\), meaning that it's value on the graph is \(-4\), meaning it `shifts left 4`

As well as that, you can see that \(k\) is \(-5\), meaning that the graph `shifts down 5`

Now, there is a negative next to the square root, meaning that the graph is `flipped across the x-axis`

Y-axis flips would only occur if \(s(x)\) was negative, meaning that there is `no change` in it's y-axis placement

Answer 3

Okay , what about vertical stretch/compress and the vertical shift ?

Answer 4

@extrinix

Answer 5

As shown, the equation \(f(x)=a\sqrt{x-h}+k\)

\(a\) represents the stretch or compression of the equation, but as \(a\) is equal to 1 on your equation, there is `no change` in it's stretch or compression

Answer 6

okay good

Answer 7

👍👍

Answer 8

Consider the following function.

\[u(x) =-\sqrt{x+4}\]

Determine the domain and range of the original function. Express your answer in interval notation.

Answer 9

Use my previous post as an example and try it for yourself