Question

Complete the table for the function y= 8(1/4)^x.
x y
-2 __
-1 __
0 __
1 __
Now, graph the function.
Plot two points to graph the function

Answer 1

To complete the table for the function \( y = 8\left(\frac{1}{4}\right)^x \), we can calculate the values of \( y \) for the given values of \( x \).

1. **For \( x = -2 \)**:
\[
y = 8\left(\frac{1}{4}\right)^{-2} = 8 \times 4^2 = 8 \times 16 = 128
\]

2. **For \( x = -1 \)**:
\[
y = 8\left(\frac{1}{4}\right)^{-1} = 8 \times 4^1 = 8 \times 4 = 32
\]

3. **For \( x = 0 \)**:
\[
y = 8\left(\frac{1}{4}\right)^{0} = 8 \times 1 = 8
\]

4. **For \( x = 1 \)**:
\[
y = 8\left(\frac{1}{4}\right)^{1} = 8 \times \frac{1}{4} = 2
\]

Now let's fill out the table:

| x | y |
| --- | --- |
| -2 | 128 |
| -1 | 32 |
| 0 | 8 |
| 1 | 2 |

### Points to graph

Now let's take two points to graph the function. We can take:

1. \( (-2, 128) \)
2. \( (1, 2) \)

### Graphing

1. The point \( (-2, 128) \) will be very high on the y-axis.
2. The point \( (1, 2) \) is much lower and easy to plot.

To visualize this, you would plot the two points on a coordinate system, then note that the function will continually decrease as \( x \) increases, due to the nature of the function \( y = 8\left(\frac{1}{4}\right)^x \), which is an exponential decay function.

If you were to graph it using a graphing tool, you would find that the curve approaches the x-axis but never touches it, representing that as \( x \to \infty \), \( y \to 0 \).