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

Feb 18, 2018

See explanation.

#### Explanation:

To graph the equation $y = {\left(\frac{1}{4}\right)}^{x}$ you can substitute some values. For example you can easily calculate:

$f \left(0\right) = 1$, $f \left(1\right) = \frac{1}{4}$, $f \left(- 1\right) = 4$.

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

If $0 < a < 1$ then $f \left(x\right) = {a}^{x}$ is decreasing in its whole domain, it goes to $+ \infty$ as $x$ goes to $- \infty$, and goes to $0$ as $x$ goes to $+ \infty$.

Using these information you get:

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

The second graph $y = {\left(\frac{1}{4}\right)}^{x} - 1$ 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]}