Question

Complete the table for the function y= 0.2^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 \( y = 0.2^x \), we will calculate the values of \( y \) for each given \( x \):

1. For \( x = -2 \):
\[
y = 0.2^{-2} = \frac{1}{0.2^2} = \frac{1}{0.04} = 25
\]

2. For \( x = -1 \):
\[
y = 0.2^{-1} = \frac{1}{0.2} = 5
\]

3. For \( x = 0 \):
\[
y = 0.2^{0} = 1
\]

4. For \( x = 1 \):
\[
y = 0.2^{1} = 0.2
\]

Now we can fill in the table:

| x | y |
|----|-----|
| -2 | 25 |
| -1 | 5 |
| 0 | 1 |
| 1 | 0.2 |

### Plotting Points

To graph the function using two points, we can select:

1. \( (-1, 5) \)
2. \( (0, 1) \)

### Graphing

Here's how you can visualize it:

1. Plot the point (-1, 5) on the graph.
2. Plot the point (0, 1) on the graph.

Given that \( 0.2^x \) is an exponential decay function, it will decrease as \( x \) increases. The curve will approach 0 as \( x \) becomes larger.

Feel free to use graph paper or graphing software to represent these points accurately!