Question

List the transformations that took place on y = 5^x that resulted in the function given.State the domain and range. [2,2pts]y=57-3 + 1(11) to

Answer 1

We have that the original function is

$y=5^x$

and after some transformations we have

$y=5^{x-3}+1$

The -3 is a shift to the right and +1 is a shift up of the original function

then we will calculate the domain of the function,

the domain is the set of all possible values that can have x in this case the domain is all the real numbers

to the range is the set of values that can have y

In this case if we graph the function we will obtain that the range is

$\mleft\{y\in R\colon y>1\mright\}$

where the red line is the original function and the blue is the one with the transformations