consider the function f(x) = 3x and a translation of f(x) named g(x). janeen created a table for select values of x. her table is shown below. what can be concluded about the relationship between the two functions? check all that apply.
the functions have the same base.
the functions have the same range.
the functions have the same exponent.
the functions have the same domain.
g(x) is a translation left 1 unit.
g(x) is a translation right 2 units.
g(x) is a translation up 2 units.

The correct options are:

So, these functions have the same range.

The functions have the same base.

The functions have the same domain.

g(x) is a translation left 1 unit.

Step-by-step explanation:

According to the table, both are exponential functions.

We have that

Lets see each affirmation:

The functions have the same base.

An exponential function has base a.

In this problems, both f and g have base 3.

The functions have the same range.

The range of f are all the values that f can assume. That is, all the positive numbers.

The range of g are all the values that g can assume. That is, also all the positive numbers.

So, these functions have the same range.

The functions have the same exponent.

An exponential function has exponent x.

f has exponent x and g has exponent x + 1. So those functions do not have the same exponent.

The functions have the same domain.

Yes, they both have x = {0,1,2,3} as domain.

g(x) is a translation left 1 unit.

g(x) = f(x+1). So yes, g(x) is a translation left 1 unit.

g(x) is a translation right 2 units.

g(x) is not f(x-2). So g(x) is not a translation right 2 units.

g(x) is a translation up 2 units.

g(x) is not f(x) + 2. So g(x) is not a translation up 2 units.

ryan had a head start of 10 meters.