Question

chapter 6 quiz
170 points possible answered: 7/17
question 8
given the equation ( y = 6 \tan ( 8 x + 56 ) )
the period is:
the horizontal shift is: units to the
add work

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Explanation:

Step1: Recall the formula for the period of \(y = A\tan(Bx - C)+D\)

The period of \(y = A\tan(Bx - C)+D\) is \(\frac{\pi}{|B|}\). For the equation \(y = 6\tan(8x + 56)=6\tan(8x-(- 56))\), here \(B = 8\).

Step2: Calculate the period

Using the formula \(\text{Period}=\frac{\pi}{|B|}\), substitute \(B = 8\). So, \(\text{Period}=\frac{\pi}{8}\).

Step3: Recall the formula for the horizontal shift of \(y = A\tan(Bx - C)+D\)

The horizontal shift of \(y = A\tan(Bx - C)+D\) is \(\frac{C}{B}\). For the equation \(y = 6\tan(8x + 56)=6\tan(8x-(-56))\), here \(B = 8\) and \(C=-56\).

Step4: Calculate the horizontal shift

Using the formula \(\text{Horizontal shift}=\frac{C}{B}\), substitute \(B = 8\) and \(C = - 56\). So, \(\text{Horizontal shift}=\frac{-56}{8}=-7\). A negative shift means a shift to the left.

Answer:

The period is \(\frac{\pi}{8}\). The horizontal shift is \(7\) units to the left.