Which statements accurately describe the function \( f(x)=3(16)^{\frac{3}{4} x} \) ? Select three options. The initial value is 3 . The domain is \( x>0 \). The range is \( y>0 \). The simplified base is 12 . The simplified base is 8 .

Let's analyze each statement about the function \( f(x) = 3(16)^{\frac{3}{4} x} \): 1. **The initial value is 3.** - **True.** The initial value is \( f(0) = 3(16)^{0} = 3 \). 2. **The domain is \( x > 0 \).** - **False.** For exponential functions like \( f(x) \), the domain is all real numbers (\( \mathbb{R} \)) because \( 16^{\frac{3}{4} x} \) is defined for any real \( x \). 3. **The range is \( y > 0 \).** - **True.** Since \( 16^{\frac{3}{4} x} \) is always positive and it's multiplied by 3, the range of \( f(x) \) is indeed \( y > 0 \). 4. **The simplified base is 12.** - **False.** To simplify the base: \[ 16^{\frac{3}{4} x} = (16^{\frac{3}{4}})^x = (2^4)^{\frac{3}{4}})^x = 2^{3x} = 8^x \] So, the simplified base is 8, not 12. 5. **The simplified base is 8.** - **True.** As shown above, the simplified base is indeed 8. **Therefore, the three correct statements are:** 1. The initial value is 3. 3. The range is \( y > 0 \). 5. The simplified base is 8. Answer: All except statements 2 and 4 are correct.