Question

Suppose you want to transform the graph of the function into the graph of the function . Which transformations should you perform?

Answer 1

Answer:

A

Step-by-step explanation:

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Answer 2

Answer:

A. Reflect the graph of the first function across x-axis, translate it $\frac{\pi}{4}$ to the left, and translate it 2 units up.

Step-by-step explanation:

We have the original function is $y=\tan (x+\frac{\pi}{4})-1$.

The new transformed function is given by  $y=-\tan (x+\frac{\pi}{2})+1$.

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 $y=-\tan (x+\frac{\pi}{4})-1$

2. This function obtained is translated $\frac{\pi}{4}$ units to the left i.e.  $y=-\tan (x+\frac{\pi}{4}+\frac{\pi}{4})-1$ i.e. $y=-\tan (x+\frac{\pi}{2})-1$

3. Finally, this new function is translated 2 units upwards i.e. $y=-\tan (x+\frac{\pi}{2})-1+2$ i.e. $y=-\tan (x+\frac{\pi}{2})+1$

Hence, after applying, 'reflection across x-axis, translation of $\frac{\pi}{4}$ to the left, and translation of 2 units up', we get the required function.