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 \( x \)
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For \( x = 0 \): \[ y = 4 \left( \frac{2}{3} \right)^0 = 4 \times 1 = 4 \] So the point is \( (0, 4) \).
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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:
- Plot the points \( (0, 4) \) and \( (2, 1.78) \).
- 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!