Question

Graph the function ​f(x)equals4xminus7.
x
​f(x)
minus2
0
2
Question content area bottom left
Part 1
Complete the table of function values below.
x
​f(x)
minus2
  
negative 15
0
  
negative 7
2
  
1
Part 2
Use the graphing tool to graph the function.

.
.
.
Question content area right
Part 1
-20
-16
-12
-8
-4
4
8
12
16
20
-20
-16
-12
-8
-4
4
8
12
16
20
x
y

Answer 1

To complete the task, let's first evaluate the function \(f(x) = 4x - 7\) at the given points in the table.

### Part 1: Completing the table of function values

1. For \(x = -2\):
\[
f(-2) = 4(-2) - 7 = -8 - 7 = -15
\]

2. For \(x = 0\):
\[
f(0) = 4(0) - 7 = 0 - 7 = -7
\]

3. For \(x = 2\):
\[
f(2) = 4(2) - 7 = 8 - 7 = 1
\]

Now, we can complete the table:

| \(x\) | \(f(x)\) |
|---------|------------|
| -2 | -15 |
| 0 | -7 |
| 2 | 1 |

### Part 2: Graphing the function

To graph the function \(f(x) = 4x - 7\), plot the points we calculated:

- \((-2, -15)\)
- \((0, -7)\)
- \((2, 1)\)

The function is linear, so you can draw a straight line through these points. The slope \(4\) indicates that for every unit increase in \(x\), \(f(x)\) increases by \(4\) units. The y-intercept is at \(-7\), indicating where the line crosses the y-axis.

Here's a simple sketch of the points on a coordinate plane:

- On the \(x\)-axis, mark points at \(-2\), \(0\), and \(2\).
- On the \(y\)-axis, mark points at \(-15\), \(-7\), and \(1\).
- Connect these points with a straight line.

If you are using a graphing tool, you'll enter the linear function \(f(x) = 4x - 7\) to generate the graph.