Discover the answers you need at Westonci.ca, a dynamic Q&A platform where knowledge is shared freely by a community of experts. Connect with a community of experts ready to provide precise solutions to your questions on our user-friendly Q&A platform. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform.
Sagot :
To graph the exponential function [tex]\( f(x) \)[/tex] using the given table values, follow these steps:
1. Understand the Data:
The table provides discrete points on the function. Here are the pairs of [tex]\((x, y)\)[/tex] coordinates:
[tex]\[ \begin{array}{|c|c|} \hline x & y \\ \hline -3 & -7.75 \\ \hline -2 & -7.5 \\ \hline -1 & -7 \\ \hline 0 & -6 \\ \hline 1 & -4 \\ \hline 2 & 0 \\ \hline 3 & 8 \\ \hline \end{array} \][/tex]
2. Setup Your Coordinate Plane:
Create a graph with [tex]\( x \)[/tex]-axis (horizontal) and [tex]\( y \)[/tex]-axis (vertical). You will need to cover the range of [tex]\( x \)[/tex] from -3 to 3 and [tex]\( y \)[/tex] from -8 to 8, based on the provided point values.
3. Plot the Points:
Using the coordinate pairs, plot each point on the graph:
- Plot [tex]\((-3, -7.75)\)[/tex]
- Plot [tex]\((-2, -7.5)\)[/tex]
- Plot [tex]\((-1, -7)\)[/tex]
- Plot [tex]\((0, -6)\)[/tex]
- Plot [tex]\((1, -4)\)[/tex]
- Plot [tex]\((2, 0)\)[/tex]
- Plot [tex]\((3, 8)\)[/tex]
4. Draw the Curve:
After plotting the points, draw a smooth curve that passes through all the points. Since these points represent an exponential function, the curve should show the typical shape of an exponential curve which increases rapidly after passing through the point where [tex]\( y = 0 \)[/tex].
5. Analyze the Graph:
As you draw the curve, observe that:
- For [tex]\( x < 0 \)[/tex], the values of [tex]\( y \)[/tex] are negative and decreasing slowly.
- At [tex]\( x = 0 \)[/tex], [tex]\( y \)[/tex] is -6.
- For [tex]\( x > 0 \)[/tex], the values of [tex]\( y \)[/tex] increase rapidly, especially from [tex]\( x = 2 \)[/tex] to [tex]\( x = 3 \)[/tex].
6. Final Touches:
Ensure your curve is smooth and accurately represents the shape suggested by the data points. Label the axes, and provide a title such as "Graph of the Exponential Function".
Here is a rough sketch of the plot:
```
10|
9|
8|
7|
6|
5|
4|
3|
2|
1|
0|
-1|
-2|
-3|
-4|
-5|
-6|
-7|
-8|
-9|________________________________________________*__________
-3 -2 -1 0 1 2 3
```
By following these steps, you can accurately graph the exponential function using the provided table values.
1. Understand the Data:
The table provides discrete points on the function. Here are the pairs of [tex]\((x, y)\)[/tex] coordinates:
[tex]\[ \begin{array}{|c|c|} \hline x & y \\ \hline -3 & -7.75 \\ \hline -2 & -7.5 \\ \hline -1 & -7 \\ \hline 0 & -6 \\ \hline 1 & -4 \\ \hline 2 & 0 \\ \hline 3 & 8 \\ \hline \end{array} \][/tex]
2. Setup Your Coordinate Plane:
Create a graph with [tex]\( x \)[/tex]-axis (horizontal) and [tex]\( y \)[/tex]-axis (vertical). You will need to cover the range of [tex]\( x \)[/tex] from -3 to 3 and [tex]\( y \)[/tex] from -8 to 8, based on the provided point values.
3. Plot the Points:
Using the coordinate pairs, plot each point on the graph:
- Plot [tex]\((-3, -7.75)\)[/tex]
- Plot [tex]\((-2, -7.5)\)[/tex]
- Plot [tex]\((-1, -7)\)[/tex]
- Plot [tex]\((0, -6)\)[/tex]
- Plot [tex]\((1, -4)\)[/tex]
- Plot [tex]\((2, 0)\)[/tex]
- Plot [tex]\((3, 8)\)[/tex]
4. Draw the Curve:
After plotting the points, draw a smooth curve that passes through all the points. Since these points represent an exponential function, the curve should show the typical shape of an exponential curve which increases rapidly after passing through the point where [tex]\( y = 0 \)[/tex].
5. Analyze the Graph:
As you draw the curve, observe that:
- For [tex]\( x < 0 \)[/tex], the values of [tex]\( y \)[/tex] are negative and decreasing slowly.
- At [tex]\( x = 0 \)[/tex], [tex]\( y \)[/tex] is -6.
- For [tex]\( x > 0 \)[/tex], the values of [tex]\( y \)[/tex] increase rapidly, especially from [tex]\( x = 2 \)[/tex] to [tex]\( x = 3 \)[/tex].
6. Final Touches:
Ensure your curve is smooth and accurately represents the shape suggested by the data points. Label the axes, and provide a title such as "Graph of the Exponential Function".
Here is a rough sketch of the plot:
```
10|
9|
8|
7|
6|
5|
4|
3|
2|
1|
0|
-1|
-2|
-3|
-4|
-5|
-6|
-7|
-8|
-9|________________________________________________*__________
-3 -2 -1 0 1 2 3
```
By following these steps, you can accurately graph the exponential function using the provided table values.
We hope this information was helpful. Feel free to return anytime for more answers to your questions and concerns. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Westonci.ca is your go-to source for reliable answers. Return soon for more expert insights.
