Question
set up a table and graph the function
f(x) = 2x+1
f(x) = 2x+1
Answers
GPT-4o mini
To set up a table and graph the function \( f(x) = 2x + 1 \), we will first create a table of values for the function by selecting some values for \( x \), and then we can graph the function based on these values.
### Step 1: Create a Table of Values
Let's choose some values for \( x \): -2, -1, 0, 1, 2.
Now we will compute \( f(x) \) for each selected value:
\[
\begin{array}{|c|c|}
\hline
x & f(x) = 2x + 1 \\
\hline
-2 & f(-2) = 2(-2) + 1 = -4 + 1 = -3 \\
-1 & f(-1) = 2(-1) + 1 = -2 + 1 = -1 \\
0 & f(0) = 2(0) + 1 = 0 + 1 = 1 \\
1 & f(1) = 2(1) + 1 = 2 + 1 = 3 \\
2 & f(2) = 2(2) + 1 = 4 + 1 = 5 \\
\hline
\end{array}
\]
### Step 2: Table of Values
Here's the table of values we computed:
\[
\begin{array}{|c|c|}
\hline
\text{x} & \text{f(x)} \\
\hline
-2 & -3 \\
-1 & -1 \\
0 & 1 \\
1 & 3 \\
2 & 5 \\
\hline
\end{array}
\]
### Step 3: Graph the Function
To graph the function \( f(x) = 2x + 1 \):
1. Plot each point from the table on a Cartesian plane.
2. The points to plot are:
- (-2, -3)
- (-1, -1)
- (0, 1)
- (1, 3)
- (2, 5)
3. Connect the points with a straight line since this is a linear function.
The linear equation can be represented graphically as a straight line, and you can see that it slopes upward due to the positive coefficient of \( x \) (which is 2).
### Graph
If you were to sketch or use graphing software, it would look something like this:
```
y
|
6|
5| *
4|
3| *
2|
1| *
0|___________________________ x
-2 -1 0 1 2
-1| *
-2| *
-3|*
```
The line will continue infinitely in both directions beyond the points plotted. The y-intercept occurs at \( (0, 1) \), and the slope indicates that for every increase of 1 in \( x \), \( f(x) \) increases by 2.
### Step 1: Create a Table of Values
Let's choose some values for \( x \): -2, -1, 0, 1, 2.
Now we will compute \( f(x) \) for each selected value:
\[
\begin{array}{|c|c|}
\hline
x & f(x) = 2x + 1 \\
\hline
-2 & f(-2) = 2(-2) + 1 = -4 + 1 = -3 \\
-1 & f(-1) = 2(-1) + 1 = -2 + 1 = -1 \\
0 & f(0) = 2(0) + 1 = 0 + 1 = 1 \\
1 & f(1) = 2(1) + 1 = 2 + 1 = 3 \\
2 & f(2) = 2(2) + 1 = 4 + 1 = 5 \\
\hline
\end{array}
\]
### Step 2: Table of Values
Here's the table of values we computed:
\[
\begin{array}{|c|c|}
\hline
\text{x} & \text{f(x)} \\
\hline
-2 & -3 \\
-1 & -1 \\
0 & 1 \\
1 & 3 \\
2 & 5 \\
\hline
\end{array}
\]
### Step 3: Graph the Function
To graph the function \( f(x) = 2x + 1 \):
1. Plot each point from the table on a Cartesian plane.
2. The points to plot are:
- (-2, -3)
- (-1, -1)
- (0, 1)
- (1, 3)
- (2, 5)
3. Connect the points with a straight line since this is a linear function.
The linear equation can be represented graphically as a straight line, and you can see that it slopes upward due to the positive coefficient of \( x \) (which is 2).
### Graph
If you were to sketch or use graphing software, it would look something like this:
```
y
|
6|
5| *
4|
3| *
2|
1| *
0|___________________________ x
-2 -1 0 1 2
-1| *
-2| *
-3|*
```
The line will continue infinitely in both directions beyond the points plotted. The y-intercept occurs at \( (0, 1) \), and the slope indicates that for every increase of 1 in \( x \), \( f(x) \) increases by 2.