Question

use technology to find points and then graph the function $y = 2^{x - 3} + 1$, following the instructions below.
equation of asymptote:
$y = \boxed{+1}$
plot at least four points with integer coordinates that fit on the axes below. click a point to
delete it.

Explanation:

Step1: Identify horizontal asymptote

For $y = b^{x-h}+k$, asymptote is $y=k$. Here $k=1$, so $y=1$.

Step2: Calculate point at $x=1$

Substitute $x=1$:
$y=2^{1-3}+1=2^{-2}+1=\frac{1}{4}+1=1.25$
Point: $(1, 1.25)$

Step3: Calculate point at $x=2$

Substitute $x=2$:
$y=2^{2-3}+1=2^{-1}+1=\frac{1}{2}+1=1.5$
Point: $(2, 1.5)$

Step4: Calculate point at $x=3$

Substitute $x=3$:
$y=2^{3-3}+1=2^{0}+1=1+1=2$
Point: $(3, 2)$

Step5: Calculate point at $x=4$

Substitute $x=4$:
$y=2^{4-3}+1=2^{1}+1=2+1=3$
Point: $(4, 3)$

Step6: Calculate point at $x=5$

Substitute $x=5$:
$y=2^{5-3}+1=2^{2}+1=4+1=5$
Point: $(5, 5)$

Answer:

Equation of asymptote: $y=1$
Points to plot: $(1, 1.25)$, $(2, 1.5)$, $(3, 2)$, $(4, 3)$ (or $(5, 5)$ as an additional point)