Question

Complete the table for the function y= 0.1^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 \( y = 0.1^x \), we can substitute each value of \( x \) to find the corresponding \( y \) values.

1. For \( x = -2 \):
\[
y = 0.1^{-2} = \frac{1}{0.1^2} = \frac{1}{0.01} = 100
\]

2. For \( x = -1 \):
\[
y = 0.1^{-1} = \frac{1}{0.1} = 10
\]

3. For \( x = 0 \):
\[
y = 0.1^{0} = 1
\]

4. For \( x = 1 \):
\[
y = 0.1^{1} = 0.1
\]

Now, we can fill out the table:

| x | y |
|-----|--------|
| -2 | 100 |
| -1 | 10 |
| 0 | 1 |
| 1 | 0.1 |

### Graphing the Function

To graph the function \( y = 0.1^x \), we can plot the points we calculated:

- Point for \( ( -2, 100 ) \)
- Point for \( ( -1, 10 ) \)
- Point for \( ( 0, 1 ) \)
- Point for \( ( 1, 0.1 ) \)

Let's plot two of these points:

- **Point 1**: \( (-2, 100) \)
- **Point 2**: \( (0, 1) \)

It's important to note that as \( x \) increases, \( y \) decreases, tending toward zero but never actually reaching it. The graph of \( y = 0.1^x \) will decrease rapidly for positive values of \( x \) and increase sharply for negative values of \( x \).

If you draw this on a coordinate grid, you would see that the curve approaches the x-axis but does not touch it, illustrating the exponential decay of the function.