Answer:
A. Reflect the graph of the first function across x-axis, translate it [tex]\frac{\pi}{4}[/tex] to the left, and translate it 2 units up.
Step-by-step explanation:
We have the original function is [tex]y=\tan (x+\frac{\pi}{4})-1[/tex].
The new transformed function is given by [tex]y=-\tan (x+\frac{\pi}{2})+1[/tex].
So, we can see that the following sequence of transformations have been applied to the original function:
1. The function f(x) is reflected about x-axis i.e. f(x) becomes -f(x), which gives [tex]y=-\tan (x+\frac{\pi}{4})-1[/tex]
2. This function obtained is translated [tex]\frac{\pi}{4}[/tex] units to the left i.e. [tex]y=-\tan (x+\frac{\pi}{4}+\frac{\pi}{4})-1[/tex] i.e. [tex]y=-\tan (x+\frac{\pi}{2})-1[/tex]
3. Finally, this new function is translated 2 units upwards i.e. [tex]y=-\tan (x+\frac{\pi}{2})-1+2[/tex] i.e. [tex]y=-\tan (x+\frac{\pi}{2})+1[/tex]
Hence, after applying, 'reflection across x-axis, translation of [tex]\frac{\pi}{4}[/tex] to the left, and translation of 2 units up', we get the required function.
