Question

what is the domain of the function $y = 2e^x$ graphed below?

options:

• all real numbers greater than 2
• all positive real numbers
• all negative real numbers
• all real numbers

Explanation:

Step1: Recall Domain of Exponential Function

The function \( y = 2e^x \) is an exponential function. The general form of an exponential function \( y = a e^{kx} \) (where \( a
eq0 \), \( k\) is a constant) has a domain of all real numbers because there are no restrictions on the input \( x \) (no division by zero, no even roots of negative numbers, etc.).

Step2: Analyze the Graph

Looking at the graph, the curve extends infinitely to the left (as \( x \to -\infty \)) and infinitely to the right (as \( x \to +\infty \)). This means \( x \) can take any real - number value.

Answer:

all real numbers (the option: all real numbers)