Question

1. consider the curve $y = 2\left(4^x\

ight)$. 6a determine the $y$-intercept of the exponential curve. \\( y = 2 \\) 5 you got it! 6b can the function value ever be negative? yes no

Explanation:

Step1: Analyze the properties of exponential functions

For any exponential function of the form \(y = a\cdot b^{x}\) (\(a
eq0\), \(b>0\), \(b
eq1\)), the range is \(y>0\) when \(a>0\). In the given function \(y = 2(4^{x})\), \(a = 2>0\) and \(b = 4>0\).

Step2: Conclude the function value

Since \(4^{x}>0\) for all real - valued \(x\) (because for any real number \(x\), \(b^{x}=\text{e}^{x\ln b}\) and \(\text{e}^{u}>0\) for all real \(u\)), and \(a = 2>0\), then \(y=2(4^{x})=2\times(\text{positive number})>0\) for all \(x\in R\).

Answer:

B. No