Question

Which graph represents the function f(x)=(13)−x?

Answer 1

Bottom left

Explanation:

Let's look at it as (1/3)^x first. This function would have a y-intercept of (0,1) (because (1/3)^0 is 1), and would then become (1/3) times smaller for every 1 unit increment of x. This would look like the top left graph in these options. However, we are given (1/3)^-x, which means, in terms of transformations, that the graph is flipped across the y-axis. Algebraically, this looks like (1/3)^(-x) which equals to
`(1)/((1/3)^x)`, which simplifies down to 3^x, which would look like the bottom left graph.