Question

question 5 of 10
the range of the function given below is the set of all positive real numbers greater than 5.

$r(x) = 5 + 4^x$

a. true
b. false

Explanation:

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

The function \(y = 4^x\) is an exponential function with base \(4>1\). For any real number \(x\), the range of \(4^x\) is \(y>0\) (since exponential functions of the form \(a^x\) with \(a > 0,a
eq1\) have a range of positive real numbers).

Step2: Analyze the range of \(R(x)=5 + 4^x\)

If we add 5 to the function \(4^x\), we are shifting the graph of \(4^x\) up by 5 units. So the range of \(R(x)=5 + 4^x\) will be the set of all real numbers \(y\) such that \(y>5\) (because \(4^x>0\) implies \(5 + 4^x>5\)).

Answer:

A. True