Question

graph f(x) = (1/3)^x+1
​

Answer 1

Answer:

The graph is attached below.

Step-by-step explanation:

Given the function

$f\left(x\right)\:=\:\left(1/3\right)^x+1$

Exponentiation function have a horizontal Asymptotes.

Finding the horizontal Asymptotes

$\mathrm{Exponential\:function\:of\:the\:form}\:f\left(x\right)\:=c\cdot \:n^{ax+b}+k\:$

$\mathrm{has\:a\:horizontal\:asymptote}\:y=k\:$

$k=1$

$\mathrm{The\:horizontal\:asymptote\:is:}$

$y=1$

Finding y-intercepts

$y\mathrm{-intercept\:is\:the\:point\:on\:the\:graph\:where\:}x=0$

$y=\left(\frac{1}{3}\right)^0+1$

$\mathrm{Apply\:rule}\:a^0=1,\:a\ne \:0$

$\left(\frac{1}{3}\right)^0=1$

$y=1+1$

$\mathrm{Add\:the\:numbers:}\:1+1=2$

$y=2$

$\mathrm{Y\:Intercepts}:\:\left(0,\:2\right)$

The graph is attached below.