Question

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

Answer 1

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.