How do you graph #y=2*8^x#? What is the #y#-intercept and the domain and range?

1 Answer
Dec 9, 2017

Graph as shown below

Explanation:

The first thing we can do is simplify #2*8^x #

We know #8 = 2^3#

So hence #y = 2*8^x => y= 2* (2^3)^x #

#=>y= 2*2^(3x)#

#=> y = 2^(3x+1)#

we know what #y=2^x # looks like:

graph{y = 2^x [-10.085, 9.915, -1.44, 8.56]}

But #2^(3x+1) = 2^(3(x+1/3 ))#

What is a stretch of #2^x#, by #1/3# in the x direction, and then a translation of #(-1/3,0)#

Hence we yield:

graph{2^(3x+1) [-10.21, 9.79, -1.52, 8.48]}

We can see from this graph that it has a domain of #x in RR# it is defined for all #x#

We can also see that it has a range of: #y>0# it's always positive, but never equalls #0#.

It hence has a #y#-intercept of #(0,2) # as at #x=0#: # y=2#, we can see this by simply substituing #x=0#