Question

Graph this function.
y=3 + 1/2^x
Plot two points to graph the function.

Answer 1

To graph the function \( y = 3 + \frac{1}{2^x} \), we can start by calculating a couple of points for different values of \( x \).

1. **Choose \( x = 0 \)**:
\[
y = 3 + \frac{1}{2^0} = 3 + 1 = 4
\]
So, one point is \( (0, 4) \).

2. **Choose \( x = 2 \)**:
\[
y = 3 + \frac{1}{2^2} = 3 + \frac{1}{4} = 3 + 0.25 = 3.25
\]
So, another point is \( (2, 3.25) \).

Now we have two points for the graph: \( (0, 4) \) and \( (2, 3.25) \).

### Graphing the Function
- The first point \( (0, 4) \) indicates that when \( x = 0 \), \( y \) is \( 4 \).
- The second point \( (2, 3.25) \) shows that when \( x = 2 \), \( y \) decreases to \( 3.25 \).

### Behavior of the Function
As \( x \) increases, \( \frac{1}{2^x} \) decreases, which means \( y \) approaches \( 3 \) but never reaches it, indicating a horizontal asymptote at \( y = 3 \).

### Summary of Points
1. \( (0, 4) \)
2. \( (2, 3.25) \)

These points can help you sketch the graph for the function \( y = 3 + \frac{1}{2^x} \), showing its decreasing nature as \( x \) increases.