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: Recall the range of \( e^x \)

The exponential function \( y = e^x \) has a range of all real numbers greater than 0, i.e., \( (0, +\infty) \).

Step2: Analyze the function \( y = 4e^x \)

When we multiply the function \( e^x \) by 4, we are vertically stretching the graph of \( e^x \) by a factor of 4. Since multiplying a positive number (the output of \( e^x \)) by 4 will still result in a positive number, and as \( e^x \) can get arbitrarily close to 0 (but never 0) and arbitrarily large, multiplying by 4 will make the output of \( 4e^x \) also get arbitrarily close to 0 (but never 0) and arbitrarily large. So the range of \( y = 4e^x \) is all real numbers greater than 0.

Answer:

all real numbers greater than 0