Question

use the graph of the function ( y = 4 ^ { x } ) to answer the following questions. the domain of the function is negative infinity to positive infinity because an exponent can be any real number. complete the range of the function is to because ( 4 ^ { x } ) is always positive. done

Explanation:

Step1: Analyze the range of an exponential function

For the function \(y = a^{x}\) (\(a>0,a
eq1\)), when \(x\to-\infty\), \(y = 4^{x}=\frac{1}{4^{-x}}\to0\) (but \(y>0\)), and when \(x\to+\infty\), \(y = 4^{x}\to+\infty\).

Step2: Determine the range

Since \(4^{x}>0\) for all real \(x\), the lower - bound of the range is \(0\) (not including \(0\)) and the upper - bound is \(+\infty\).

Answer:

The range of the function is \(0\) to \(+\infty\)