Question

graph the function $y = 2^{x - 2} + 1$ using the given table of values and following the instructions below.

$x$	$y$		$x$	$y$		$x$	$y$
-9	1.0004883		-2	1.0625		5	9
-8	1.0009766		-1	1.125		6	17
-7	1.0019531		0	1.25		7	33
-6	1.0039063		1	1.5		8	65
-5	1.0078125		2	2		9	129
-4	1.015625		3	3		10	257

equation of asymptote:
$y = \square$

Explanation:

Step1: Recall Exponential Function Asymptote

For an exponential function of the form \( y = a^{x - h} + k \), the horizontal asymptote is \( y = k \).

Step2: Identify \( k \) in Given Function

The given function is \( y = 2^{x - 2} + 1 \). Comparing with \( y = a^{x - h} + k \), we see that \( k = 1 \). So the horizontal asymptote is \( y = 1 \).

Answer:

\( 1 \)