To graph the function \( y = 5(4)^x \), we can choose a couple of values for \( x \) to find corresponding \( y \) values. Let's choose \( x = 0 \) and \( x = 1 \).
Calculating Points:
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For \( x = 0 \): \[ y = 5(4)^0 = 5(1) = 5 \] So, the first point is \( (0, 5) \).
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For \( x = 1 \): \[ y = 5(4)^1 = 5(4) = 20 \] So, the second point is \( (1, 20) \).
Points to Plot:
- \( (0, 5) \)
- \( (1, 20) \)
Graphing:
To create the graph:
- Plot the point \( (0, 5) \) on the coordinate plane, which is on the y-axis.
- Plot the point \( (1, 20) \), which is one unit to the right and twenty units up from the origin.
Characteristics of the Function:
- The function is an exponential function that increases rapidly as \( x \) increases.
- As \( x \) approaches negative values, \( y \) approaches 0 but never actually reaches it.
You can sketch the curve starting from near the x-axis for negative \( x \), passing through the points you plotted, and increasing sharply as \( x \) becomes larger.
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