Question

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

ight)$. 6d what is the range of the function? give your answer as an inequality.

Explanation:

Step1: Analyze the exponential function \(4^x\)

For any real number \(x\), the exponential function \(a^x\) (\(a = 4>0\)) has the property that \(4^x>0\). This is because \(y = a^x\), when \(a>0\) and \(a
eq1\), for all \(x\in R\), \(a^x=\frac{1}{a^{-x}}\) (if \(x < 0\)), \(a^x = 1\) (if \(x = 0\)), and \(a^x=a\times a\times\cdots\times a\) (\(n\) times, if \(x=n,n\in N\)).

Step2: Analyze the function \(y = 2\times4^x\)

Since \(4^x>0\), when we multiply \(4^x\) by \(2\) (a positive constant), we use the property of inequalities. If \(u>0\) and \(c>0\), then \(cu>0\). Let \(u = 4^x\) and \(c = 2\). So \(y=2\times4^x>0\)

Answer:

\(y>0\)