Question

I need a little help with this, I graphed it but I’m still stuck. I just need an example :)

Answer 1

First, consider that we need to transform y=sqrt(x) into y=sqrt(-x). For this, we need to reflect the function f(x) across the y-axis. After that reflection, we end up with:

$y=\sqrt[]{-x},\text{ y-axis reflection}$

Now, we need to implement a translation to the left by 5 units. After implementing this, we obtain:

$y=\sqrt[]{(-x-5)},\text{ horizontal translation to the left by 5 units}$

Then, the constant 2. A constant in that position means that the function is vertically stretched by that constant. In this case, the function is vertically stretched by 2 units.

$y=2\sqrt[\square]{-x-5},\text{ vertical stretch by 2 units}$

Finally, a constant in the position where +3 represents a vertical shift (Upwards if the constant is positive and downwards if the constant is negative). Then, in this case, it is a vertical translation upwards by 3 units.

$y=2\sqrt[]{-x-5}+3,\text{ vertical translation upwards by 3 units}$