Question

Create a table of values for the function f(x)=4x−3
, and graph the function. What is the y
-intercept?(1 poi

Answer 1

To create a table of values for the function \( f(x) = 4x - 3 \), we'll choose several values for \( x \), calculate \( f(x) \) for those values, and then list the results.

### Table of Values

| \( x \) | \( f(x) = 4x - 3 \) |
|---------|---------------------|
| -2 | \( 4(-2) - 3 = -8 - 3 = -11 \) |
| -1 | \( 4(-1) - 3 = -4 - 3 = -7 \) |
| 0 | \( 4(0) - 3 = 0 - 3 = -3 \) |
| 1 | \( 4(1) - 3 = 4 - 3 = 1 \) |
| 2 | \( 4(2) - 3 = 8 - 3 = 5 \) |

### Table Summary

Here is the completed table:

| \( x \) | \( f(x) \) |
|---------|-------------|
| -2 | -11 |
| -1 | -7 |
| 0 | -3 |
| 1 | 1 |
| 2 | 5 |

### Finding the y-intercept

To find the y-intercept of the function, we evaluate \( f(x) \) at \( x = 0 \):

\[
f(0) = 4(0) - 3 = -3
\]

Thus, the y-intercept is \( (0, -3) \).

### Graphing the Function

You can graph the function using the points from the table. Plot the following points on a coordinate plane:

- \( (-2, -11) \)
- \( (-1, -7) \)
- \( (0, -3) \)
- \( (1, 1) \)
- \( (2, 5) \)

Connect these points with a straight line, as this is a linear function.

### Summary

- **Function:** \( f(x) = 4x - 3 \)
- **Table of Values:**
- \( (-2, -11) \)
- \( (-1, -7) \)
- \( (0, -3) \) (y-intercept)
- \( (1, 1) \)
- \( (2, 5) \)
- **Y-intercept:** \( (0, -3) \)

If you need a visual representation, you can use graphing software or graphing tools available online.