Question

Graph this function.
y=4(2/3)^x
Plot two points to graph the function.

Answer 1

To graph the function \( y = 4 \left( \frac{2}{3} \right)^x \), we can find two points by selecting different values for \( x \) and calculating the corresponding \( y \) values.

### Step 1: Select values for \( x \)
Let's choose \( x = 0 \) and \( x = 2 \) for easier calculations.

### Step 2: Calculate \( y \) for each selected \( x \)

1. **For \( x = 0 \)**:
\[
y = 4 \left( \frac{2}{3} \right)^0 = 4 \times 1 = 4
\]
So the point is \( (0, 4) \).

2. **For \( x = 2 \)**:
\[
y = 4 \left( \frac{2}{3} \right)^2 = 4 \times \frac{4}{9} = \frac{16}{9} \approx 1.78
\]
So the point is \( (2, \frac{16}{9}) \).

### Step 3: Summary of points
- The first point is \( (0, 4) \).
- The second point is \( (2, \frac{16}{9}) \) or approximately \( (2, 1.78) \).

### Step 4: Graphing the function
To graph the function:

1. Plot the points \( (0, 4) \) and \( (2, 1.78) \).
2. Draw a smooth curve that approaches zero as \( x \) increases, since the base of the exponent \( \frac{2}{3} \) is less than 1 (the function will decay).

### Visual Representation
Although I can't draw directly, you would see a decreasing curve starting from \( y = 4 \) when \( x = 0 \) and dropping towards the horizontal axis as \( x \) increases. Make sure to label the points and the axes appropriately!