Question

Complete the table for the function y=9^x
x y
–1
0
1
2



Now, graph the function.
Plot two points to graph the function.

Answer 1

To complete the table for the function \( y = 9^x \), we will calculate the values of \( y \) for each given value of \( x \):

1. For \( x = -1 \):
\[
y = 9^{-1} = \frac{1}{9} \approx 0.1111
\]

2. For \( x = 0 \):
\[
y = 9^0 = 1
\]

3. For \( x = 1 \):
\[
y = 9^1 = 9
\]

4. For \( x = 2 \):
\[
y = 9^2 = 81
\]

Now, we can complete the table:

| \( x \) | \( y \) |
|---------|------------|
| -1 | 0.1111 |
| 0 | 1 |
| 1 | 9 |
| 2 | 81 |

### Two Points to Graph the Function

From the table, we can choose the following two points to graph the function:
1. \( (0, 1) \)
2. \( (1, 9) \)

### Graphing the Function

To plot the two points:
- Plot the point \( (0, 1) \) on the coordinate plane.
- Plot the point \( (1, 9) \).

The graph of the function \( y = 9^x \) will show an exponential growth curve, starting from \( (0, 1) \) and rapidly increasing as \( x \) increases.

If you were to graph a larger portion of this function, you would see that it approaches \( 0 \) as \( x \) goes to \( -\infty \) and rises steeply for positive values of \( x \).