Question

what is the range of the function ( y = 4e^{x} )?
all real numbers greater than 0
all real numbers less than 0
all real numbers less than 4
all real numbers greater than 4

Explanation:

Step1: Analyze the range of \(e^x\)

The exponential function \(e^x\) has a range of \((0,\infty)\), i.e., \(e^x>0\) for all real \(x\).

Step2: Analyze the range of \(4e^x\)

Since \(e^x>0\), when we multiply by \(4\) (a positive constant), the inequality remains the same. So \(4e^x>0\).

Answer:

all real numbers greater than \(0\)