Question

Graph this function.
y=9(2/3)^x
Plot two points to graph the function.

Answer 1

To graph the function \( y = 9 \left( \frac{2}{3} \right)^x \), we will plot two points by choosing values for \( x \) and calculating the corresponding \( y \) values.

### Step 1: Choose values for \( x \)
Let's choose two values for \( x \):
- \( x = 0 \)
- \( x = 3 \)

### Step 2: Calculate corresponding \( y \) values
1. **For \( x = 0 \)**:
\[
y = 9 \left( \frac{2}{3} \right)^0 = 9 \times 1 = 9
\]
So the point is \( (0, 9) \).

2. **For \( x = 3 \)**:
\[
y = 9 \left( \frac{2}{3} \right)^3 = 9 \times \left( \frac{8}{27} \right) = \frac{72}{27} = \frac{8}{3} \approx 2.67
\]
So the point is \( (3, \frac{8}{3}) \).

### Points to Plot
- Point 1: \( (0, 9) \)
- Point 2: \( (3, 2.67) \)

### Step 3: Graph the Function
To graph the function:
- Start by plotting the points \( (0, 9) \) and \( (3, \frac{8}{3}) \).
- Since the base of the exponent \( \frac{2}{3} \) is less than 1, the function will decrease as \( x \) increases. The general shape of the graph would start at \( (0, 9) \) and move downward to the right.

### Graph (Visual Representation)
You can visualize the graph as follows:

```
y
|
10| * (0, 9)
9|
8|
7|
6|
5|
4|
3| * (3, 2.67)
2|
1|
0|_______________________
0 1 2 3 4 5 x
```

### Summary:
- The function \( y = 9 \left( \frac{2}{3} \right)^x \) starts high at \( y = 9 \) when \( x = 0 \) and falls downwards as \( x \) increases.
- Two points plotted are \( (0, 9) \) and \( (3, \frac{8}{3}) \).