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Graph this function.

y=2(7)^x
Plot two points to graph the function.

1 answer

To graph the function \( y = 2(7)^x \), we can first calculate a couple of points by choosing some values for \( x \).

Step 1: Calculate Points

Let's choose two values for \( x \):

  1. When \( x = 0 \): \[ y = 2(7)^0 = 2 \cdot 1 = 2 \] So the point is \( (0, 2) \).

  2. When \( x = 1 \): \[ y = 2(7)^1 = 2 \cdot 7 = 14 \] So the point is \( (1, 14) \).

Step 2: Points Summary

We have the following points to plot:

  • \( (0, 2) \)
  • \( (1, 14) \)

Step 3: Graph the Function

Now, we can plot these points on a Cartesian plane:

  1. Plot the point \( (0, 2) \).
  2. Plot the point \( (1, 14) \).

Step 4: Graph Characteristics

The graph of the function \( y = 2(7)^x \) is an exponential function, which means:

  • It will increase rapidly as \( x \) increases because the base \( 7 \) is greater than \( 1 \).
  • As \( x \) approaches negative values, \( y \) will approach \( 0 \), but never actually reach it (horizontal asymptote).

You can sketch the curve starting near the horizontal axis (for negative values of \( x \)), going through the points \( (0, 2) \) and \( (1, 14) \), and rising steeply as \( x \) increases.

Conclusion

This gives you enough information to graph the function \( y = 2(7)^x \). If you have graphing tools or graph paper, you can use the points we've calculated and draw in the shape of the exponential growth.