Question

Set up a table and Graph the function:
f(x) = 2x + 1

Answer 1

To set up a table for the function \( f(x) = 2x + 1 \), we will choose a range of \( x \) values and calculate the corresponding \( f(x) \) values.

### Table of Values

| \( x \) | \( f(x) = 2x + 1 \) |
|---------|---------------------|
| -2 | \( f(-2) = 2(-2) + 1 = -4 + 1 = -3 \) |
| -1 | \( f(-1) = 2(-1) + 1 = -2 + 1 = -1 \) |
| 0 | \( f(0) = 2(0) + 1 = 0 + 1 = 1 \) |
| 1 | \( f(1) = 2(1) + 1 = 2 + 1 = 3 \) |
| 2 | \( f(2) = 2(2) + 1 = 4 + 1 = 5 \) |
| 3 | \( f(3) = 2(3) + 1 = 6 + 1 = 7 \) |

### Values from the Table

From the table, we obtain the following values:

- \( f(-2) = -3 \)
- \( f(-1) = -1 \)
- \( f(0) = 1 \)
- \( f(1) = 3 \)
- \( f(2) = 5 \)
- \( f(3) = 7 \)

### Graphing the Function

To graph \( f(x) = 2x + 1 \), we'll plot the points from the table on a coordinate system and draw a straight line through the points since this is a linear function.

1. **Plot the Points:**
- Point (-2, -3)
- Point (-1, -1)
- Point (0, 1)
- Point (1, 3)
- Point (2, 5)
- Point (3, 7)

2. **Draw the Line:**
Connect the points with a straight line extending in both directions.

### Graph

Since I can't create a visual graph directly, here’s a description of how you might plot it manually:

- Draw a horizontal line for the x-axis and a vertical line for the y-axis, labeling them appropriately.
- Mark the points from the table on the graph.
- Use a ruler to draw a straight line that goes through all the points.

This line will slope upward, indicating that the function is increasing as \( x \) increases. The slope of the line is 2, which indicates that for every unit increase in \( x \), \( f(x) \) increases by 2 units.

### Conclusion

The function \( f(x) = 2x + 1 \) is a linear function with a slope of 2 and a y-intercept of 1. The table captures a few key points to help visualize the graph.