Question

Graph this function.
y=(1/4)^x
Plot two points to graph the function.

Answer 1

The function \( y = \left( \frac{1}{4} \right)^x \) is an exponential decay function. To graph this function and plot two points, we can choose values for \( x \) and calculate the corresponding \( y \) values.

### Points to Plot:

1. **When \( x = 0 \)**:
\[
y = \left( \frac{1}{4} \right)^0 = 1
\]
So, the point is \( (0, 1) \).

2. **When \( x = 2 \)**:
\[
y = \left( \frac{1}{4} \right)^2 = \frac{1}{16} = 0.0625
\]
So, the point is \( (2, 0.0625) \).

### Summary of Points:
- Point 1: \( (0, 1) \)
- Point 2: \( (2, 0.0625) \)

### Graph:
The graph of the function would start from the point \( (0, 1) \) and as \( x \) increases, the values of \( y \) decrease rapidly. The graph approaches the x-axis but never actually touches it, indicating that the function approaches zero as \( x \) tends to infinity.

### Visualization:
If you were to plot these points on a graph:
- Plot the point at \( (0, 1) \).
- Plot the point at \( (2, 0.0625) \).

Then, draw a curve that starts at \( y = 1 \) when \( x = 0 \), decreases, and heads towards but never touches the x-axis (y=0).

This would give you a good representation of the function \( y = \left( \frac{1}{4} \right)^x \).