Question

Complete the table for the function y= (1/7)^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 \( y = \left(\frac{1}{7}\right)^x \), we will calculate \( y \) for each value of \( x \).

1. **For \( x = -2 \)**:
\[
y = \left(\frac{1}{7}\right)^{-2} = 7^2 = 49
\]

2. **For \( x = -1 \)**:
\[
y = \left(\frac{1}{7}\right)^{-1} = 7^1 = 7
\]

3. **For \( x = 0 \)**:
\[
y = \left(\frac{1}{7}\right)^{0} = 1
\]

4. **For \( x = 1 \)**:
\[
y = \left(\frac{1}{7}\right)^{1} = \frac{1}{7}
\]

Now we can fill in the table:

| \( x \) | \( y \) |
|:---------:|:---------:|
| -2 | 49 |
| -1 | 7 |
| 0 | 1 |
| 1 | \(\frac{1}{7} \approx 0.14 \) |

### Graphing the function:

To graph the function \( y = \left(\frac{1}{7}\right)^x \), we can plot the points calculated:

- For \( x = -2 \), \( y = 49 \)
- For \( x = -1 \), \( y = 7 \)
- For \( x = 0 \), \( y = 1 \)
- For \( x = 1 \), \( y \approx 0.14 \)

Here are two key points to graph:

1. \( (-2, 49) \)
2. \( (0, 1) \)

### Graphing Points:
To graph, you would mark these points on a coordinate plane:

- The point \( (-2, 49) \) will be very high on the y-axis.
- The point \( (0, 1) \) will be on the y-axis.
- The point \( (1, \frac{1}{7}) \approx (1, 0.14) \) will be just above the x-axis.

The curve will decrease as x increases because the base \( \frac{1}{7} < 1 \).

If you were to create a visual:
- Draw the axes.
- Plot the points mentioned.
- Sketch a curve that approaches the x-axis as x increases and rises steeply as x decreases.

This function is an exponential decay function since the base is a fraction.