Question

what is the domain of the function \\(y = 2e^x\\) graphed below?

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

Explanation:

⚡ Using what you learned: domain and range

Step 1: Identify the definition of domain

The domain of a function is the set of all possible input values (\(x\)-values) for which the function is defined.

Step 2: Analyze the function and its graph

The given function is:

$$ y = 2e^x $$

• Algebraic analysis: The exponent \(x\) can be any real number (positive, negative, or zero) because the exponential base \(e\) can be raised to any real power.
• Graphical analysis: The graph extends infinitely to the left (towards negative infinity) and continues to grow and extend to the right (towards positive infinity). There are no breaks, holes, or vertical asymptotes restricting the \(x\)-values.

Therefore, the domain is all real numbers.

Answer:

all real numbers