Question

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

Explanation:

Step1: Analyze base exponential function

The function $e^x$ has a range of all real numbers greater than 0, i.e., $e^x > 0$ for all real $x$.

Step2: Scale by positive constant

Multiply the range by 4 (positive, so inequality direction stays): $4e^x > 4 \times 0$
Simplify: $4e^x > 0$

Answer:

all real numbers greater than 0