Question

use technology to find points and then graph the function $y = 2^x - 2$, following the instructions below.

equation of asymptote:
$y = \square$

next

answer attempt 1 out of 2

you must answer all questions above in order to submit.

Explanation:

Step1: Recall exponential function asymptote

The parent function \( y = 2^x \) has a horizontal asymptote at \( y = 0 \) (since as \( x \to -\infty \), \( 2^x \to 0 \)).

Step2: Analyze vertical shift

For the function \( y = 2^x - 2 \), we have a vertical shift down by 2 units. A vertical shift of a function \( y = f(x) \) by \( k \) units (down if \( k>0 \) in \( y = f(x)-k \)) shifts the asymptote by the same amount. So the horizontal asymptote of \( y = 2^x - 2 \) is \( y = 0 - 2=-2 \).

Answer:

\( y = -2 \)