Question
Identify the vertical stretching factor and period of the function. Answer exactly. \( f(x)=3 \tan (4 x-8) \) Vertical stretching factor: Period:
Ask by Ellis Chambers. in the United States
Feb 03,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
Vertical stretching factor: 3
Period: \( \frac{\pi}{4} \)
Solution
For the function \( f(x) = 3 \tan(4x - 8) \):
- **Vertical Stretching Factor:** The coefficient **3** directly multiplies the tangent function, indicating a vertical stretch by a factor of **3**.
- **Period:** The general period of the tangent function \( \tan(Bx) \) is \( \frac{\pi}{B} \). Here, \( B = 4 \), so the period is \( \frac{\pi}{4} \).
**Answer:**
- Vertical stretching factor: 3
- Period: \( \dfrac{\pi}{4} \)
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Simplify this solution Beyond the Answer
The vertical stretching factor of the function \( f(x) = 3 \tan(4x - 8) \) is 3, which means the graph of the tangent function is stretched vertically by a factor of 3. To find the period, we use the formula for the period of a tangent function, which is given by \( \frac{\pi}{|b|} \), where \( b \) is the coefficient of \( x \) inside the function. Here, \( b = 4 \), so the period is \( \frac{\pi}{4} \).
