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Graph this function.

y=4(6)x
Plot two points to graph the function.

1 answer

To graph the function \( y = 4(6)^x \), we begin by calculating two points for different values of \( x \).

Step 1: Calculate Points

Let's choose \( x = 0 \) and \( x = 1 \).

  1. For \( x = 0 \): \[ y = 4(6)^0 = 4(1) = 4 \] So, the first point is \( (0, 4) \).

  2. For \( x = 1 \): \[ y = 4(6)^1 = 4(6) = 24 \] Thus, the second point is \( (1, 24) \).

Step 2: Plot the Points

Now we have two points to plot:

  • \( (0, 4) \)
  • \( (1, 24) \)

Step 3: Graph the Function

  1. Plot the point \( (0, 4) \) on the graph.
  2. Plot the point \( (1, 24) \).
  3. Since this is an exponential function, we know that as \( x \) increases, \( y \) will grow rapidly. You can also calculate more points if you want to get a clearer shape of the curve.

Step 4: Draw the Curve

Connect the points smoothly in an increasing manner because exponential functions increase rapidly.

Summary of Points

  • Point 1: \( (0, 4) \)
  • Point 2: \( (1, 24) \)

The graph will show a rapid increase as \( x \) increases.