The function \( y = \left( \frac{1}{4} \right)^x \) is an exponential decay function. To graph this function and plot two points, we can choose values for \( x \) and calculate the corresponding \( y \) values.
Points to Plot:
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When \( x = 0 \): \[ y = \left( \frac{1}{4} \right)^0 = 1 \] So, the point is \( (0, 1) \).
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When \( x = 2 \): \[ y = \left( \frac{1}{4} \right)^2 = \frac{1}{16} = 0.0625 \] So, the point is \( (2, 0.0625) \).
Summary of Points:
- Point 1: \( (0, 1) \)
- Point 2: \( (2, 0.0625) \)
Graph:
The graph of the function would start from the point \( (0, 1) \) and as \( x \) increases, the values of \( y \) decrease rapidly. The graph approaches the x-axis but never actually touches it, indicating that the function approaches zero as \( x \) tends to infinity.
Visualization:
If you were to plot these points on a graph:
- Plot the point at \( (0, 1) \).
- Plot the point at \( (2, 0.0625) \).
Then, draw a curve that starts at \( y = 1 \) when \( x = 0 \), decreases, and heads towards but never touches the x-axis (y=0).
This would give you a good representation of the function \( y = \left( \frac{1}{4} \right)^x \).