Question

Which graph shows g(x) = (1/3)^x-2 +6?

Answer 1

The second graph, upper right corner.

Explanation:

The question is asking for a translated function, where the original is:

`f(x)=((1)/(3))^(x)`

So, we need to find the graph of:

`g(x)=((1)/(3))^(x-2)+6`

We observe that the expression is subtracting two units from the x, and adding 6 units to the y.

Subtracting units to x, we will translate the function to the right, in this case, 2 units.

By adding 6 units to y, we are translating the function upwards 6 units.

So, the right graph should be a similar function, translated 2 units to the right and 6 units upwards.

Therefore, the right graph is the second one, which is upper right corner.

Answer 2

Top right

Explanation:

One of the main aspects that can be used in this type of exercises is the value on the ordinates axis (another could be the 0 roots).

Let's look at the ordinates term of the function g(x) = (1/3)^x-2 +6.

We get the independent term replacing the x with 0. If we do so we have:

g(0)= 1/3^(-2)+6= 1/(3^(-2)) = 3^2 + 6 = 9+6=15

So our function must cut the ordinates axis in 15. The only one that fits this requirement is the second on the image with 4 functions (the top right).

This is the right one.