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Graph this function.

y=3(2)^x
Plot two points to graph the function.

1 answer

To graph the function \( y = 3(2)^x \), we can calculate a couple of points by choosing values for \( x \).

Step 1: Choose Values for \( x \)

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

Step 2: Calculate Corresponding \( y \) Values

  1. For \( x = 0 \): \[ y = 3(2)^0 = 3(1) = 3 \] So, the point is \( (0, 3) \).

  2. For \( x = 1 \): \[ y = 3(2)^1 = 3(2) = 6 \] So, the point is \( (1, 6) \).

Points to Plot

  • The two points are \( (0, 3) \) and \( (1, 6) \).

Step 3: Graphing the Function

To graph the function \( y = 3(2)^x \):

  1. Plot the points \( (0, 3) \) and \( (1, 6) \) on a coordinate grid.
  2. As \( x \) increases, the value of \( y \) will increase exponentially since the base of the exponent (2) is greater than 1.
  3. You could continue this process for other values of \( x \) (for example, \( x = 2 \) gives \( y = 12 \)) to see the growth of the function.

Sample Graph:

  • The y-intercept is at \( (0, 3) \).
  • As \( x \) increases, the curve rises steeply due to the exponential nature of the function.

While I cannot physically draw or display a graph here, you can plot these points on graph paper or using graphing software to visualize the function. The overall shape will be an upward curve headed towards infinity, starting from the point \( (0, 3) \).