Question

How do you graph `y=(1/4)^x` and `y=(1/4)^x-1` and how do the graphs compare?

Answer 1

See explanation.

Explanation:

To graph the equation `y=(1/4)^x` you can substitute some values. For example you can easily calculate:

`f(0)=1`, `f(1)=1/4`, `f(-1)=4`.

To graph the equation you can also use the propertes of exponential function.

If `0 < a < 1` then `f(x)=a^x` is decreasing in its whole domain, it goes to `+oo` as `x` goes to `-oo`, and goes to `0` as `x` goes to `+oo`.

Using these information you get:

graph{(1/4)^x [-25.65, 25.67, -12.82, 12.85]}

The second graph `y=(1/4)^x -1` can be obtained from the first by translating it one unit down (i.e. by a vector `vec(v)=[0;-1]`):

graph{(1/4)^x-1 [-25.65, 25.67, -12.82, 12.85]}