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:

⚡ Using what you learned: Graphing Exponential Functions

Step 1: Analyze the base exponential function

The core of the function is \( e^x \). For any real number \( x \), the natural exponential function \( e^x \) is always strictly positive:

$$ e^x > 0 $$

Step 2: Apply the vertical stretch

Multiply the inequality by the positive constant \( 4 \):

$$ y = 4e^x > 4 \cdot 0 $$

$$ y > 0 $$

This means the output values \( y \) can be any positive real number, but they can never be less than or equal to \( 0 \).

Answer:

all real numbers greater than 0