Answer :
Certainly! To graph the exponential function [tex]\( f(x) \)[/tex] given by the table of values, follow these steps:
1. Plot the Points: Use the given [tex]\((x, y)\)[/tex] pairs to plot each point on the coordinate plane.
- Point: [tex]\((-3, 12)\)[/tex]
- Point: [tex]\((-2, 4)\)[/tex]
- Point: [tex]\((-1, 0)\)[/tex]
- Point: [tex]\((0, -2)\)[/tex]
- Point: [tex]\((1, -3)\)[/tex]
- Point: [tex]\((2, -3.5)\)[/tex]
- Point: [tex]\((3, -3.75)\)[/tex]
2. Draw the Axes:
- Draw the horizontal axis (x-axis) and label it with values corresponding to [tex]\(x\)[/tex].
- Draw the vertical axis (y-axis) and label it with values corresponding to [tex]\(y\)[/tex].
3. Plot the Points on the Graph:
- Start by placing a dot at [tex]\((-3, 12)\)[/tex].
- Next, place a dot at [tex]\((-2, 4)\)[/tex].
- Continue this for each [tex]\((x, y)\)[/tex] pair provided.
4. Connect the Points: Since this is an exponential function, the points should be connected in a smooth, continuous curve that reflects the nature of an exponential graph.
5. Observe the Shape of the Graph:
- Check for any asymptotic behavior; usually, exponential functions will approach some horizontal asymptote.
By following these steps, you will have constructed a visual representation of the exponential function [tex]\( f(x) \)[/tex] using the provided data. Make sure to label the axes and the points clearly.
Here is a rough sketch based on the given points:
```
y
|
12-
|
10-
|
8-
|
6-
|
4-
|
2-
|
0----------------------------- x
|
-2-
|
-4-
|
-6-
|
-8-
|
-10-
|
-12-
```
As you can see, each point follows the sequence given in the table, and connecting them would give the shape of the exponential function.
1. Plot the Points: Use the given [tex]\((x, y)\)[/tex] pairs to plot each point on the coordinate plane.
- Point: [tex]\((-3, 12)\)[/tex]
- Point: [tex]\((-2, 4)\)[/tex]
- Point: [tex]\((-1, 0)\)[/tex]
- Point: [tex]\((0, -2)\)[/tex]
- Point: [tex]\((1, -3)\)[/tex]
- Point: [tex]\((2, -3.5)\)[/tex]
- Point: [tex]\((3, -3.75)\)[/tex]
2. Draw the Axes:
- Draw the horizontal axis (x-axis) and label it with values corresponding to [tex]\(x\)[/tex].
- Draw the vertical axis (y-axis) and label it with values corresponding to [tex]\(y\)[/tex].
3. Plot the Points on the Graph:
- Start by placing a dot at [tex]\((-3, 12)\)[/tex].
- Next, place a dot at [tex]\((-2, 4)\)[/tex].
- Continue this for each [tex]\((x, y)\)[/tex] pair provided.
4. Connect the Points: Since this is an exponential function, the points should be connected in a smooth, continuous curve that reflects the nature of an exponential graph.
5. Observe the Shape of the Graph:
- Check for any asymptotic behavior; usually, exponential functions will approach some horizontal asymptote.
By following these steps, you will have constructed a visual representation of the exponential function [tex]\( f(x) \)[/tex] using the provided data. Make sure to label the axes and the points clearly.
Here is a rough sketch based on the given points:
```
y
|
12-
|
10-
|
8-
|
6-
|
4-
|
2-
|
0----------------------------- x
|
-2-
|
-4-
|
-6-
|
-8-
|
-10-
|
-12-
```
As you can see, each point follows the sequence given in the table, and connecting them would give the shape of the exponential function.
