The period of the given function is [tex]\frac{\pi }{2}[/tex] and the phase shift is [tex]\frac{\pi }{4}[/tex] to the left.
The distance between the repetition of any function is called the period of the function.
Phase Shift is a shift when the graph of the sine function and cosine function is shifted left or right from their usual position.
According to the given problem,
For the equation y = a tan[b( x + c )], the period is equal to [tex]\frac{2\pi }{b}[/tex] and the phase shift is c.
This equation can be written as:
f(x) = 3 tan [4(x +[tex]\frac{\pi }{4}[/tex])]
In this case, b = 4, c = [tex]\frac{\pi }{4}[/tex]
Then the period = [tex]\frac{2\pi }{b}[/tex]
= [tex]\frac{\pi }{2}[/tex]
The phase shift = [tex]\frac{\pi }{4}[/tex] (to the left).
Hence, we can conclude, the period of the given function is [tex]\frac{\pi }{2}[/tex] and the phase shift is [tex]\frac{\pi }{4}[/tex] to the left.
Learn more about period and phase shift here: https://brainly.com/question/3654124
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