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Graph this function.

y=2(4)^x
Plot two points to graph the function.

1 answer

To graph the function \( y = 2(4)^x \), we can start by choosing a couple of values for \( x \) and calculating the corresponding \( y \) values.

Choosing Points:

Let's calculate the values for \( x = 0 \) and \( x = 1 \):

  1. For \( x = 0 \): \[ y = 2(4)^0 = 2(1) = 2 \] So, the point is \( (0, 2) \).

  2. For \( x = 1 \): \[ y = 2(4)^1 = 2(4) = 8 \] So, the point is \( (1, 8) \).

Points to Plot:

  • The points we have are:
    • \( (0, 2) \)
    • \( (1, 8) \)

Plotting the Function:

  1. Plot the points:

    • Point \( (0, 2) \) is where the graph crosses the y-axis.
    • Point \( (1, 8) \) shows how the function grows rapidly as \( x \) increases.

  2. Graph behavior:

    • The function \( y = 2(4)^x \) is an exponential function, which means it will increase rapidly for positive \( x \) values and approach 0 as \( x \) becomes negative.

Visual Representation:

While I can't create a visual graph directly here, you can plot the two points on a coordinate plane and draw a curve that shows the rapid increase of the function for positive \( x \) and approaches the x-axis for negative \( x \).

Here's how you can sketch it:

  • Start at point \( (0, 2) \).
  • Connect to point \( (1, 8) \) with a smooth curve that rises steeply.
  • As you extend the graph to the left (negative \( x \)), make sure it gets closer to the x-axis (y=0) but never touches it.

In a graphing tool or on graph paper, this will illustrate the exponential growth nature of the function.