Question

what is the asymptote of the parent function y=2^x?
options: x=0, x=2, y=2, y=0

Explanation:

Step1: Recall Exponential Function Asymptote

The parent exponential function is \( y = a^x \) (where \( a>0, a
eq1 \)). For \( y = 2^x \), as \( x\to-\infty \), \( 2^x\to0 \) (since a positive number to a very negative power approaches 0). So the horizontal asymptote is \( y = 0 \).

Step2: Eliminate Other Options

• \( x = 0 \) is the y - axis, not an asymptote for \( y = 2^x \) (the function crosses \( x = 0 \) at \( (0,1) \)).
• \( x = 2 \) is a vertical line; exponential functions of the form \( y=a^x \) have no vertical asymptotes (their domain is all real numbers).
• \( y = 2 \): As \( x\) changes, \( 2^x \) approaches 0 (for \( x\to-\infty \)) and grows without bound (for \( x\to\infty \)), so it doesn't approach \( y = 2 \).

Answer:

D. \( y = 0 \) (assuming the options are labeled A: \( x = 0 \), B: \( x = 2 \), C: \( y = 2 \), D: \( y = 0 \))