6) Given The Function $f(x) = -2x + 3$, Complete The Table:$\[ \begin{array}{|c|c|c|c|c|c|} \hline x & -2 & -1 & 0 & 1 & 3 \\ \hline f(x) & 7 & 5 & 3 & 1 & -3 \\ \hline \end{array} \\]
Solving the Function Table for f(x) = -2x + 3
In mathematics, functions are used to describe the relationship between variables. A function is a relation between a set of inputs (called the domain) and a set of possible outputs (called the range). In this article, we will focus on solving a function table for the given function f(x) = -2x + 3.
Understanding the Function
The given function is f(x) = -2x + 3. This is a linear function, which means it has a constant rate of change. The function can be written in the slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept. In this case, the slope (m) is -2 and the y-intercept (b) is 3.
Completing the Table
To complete the table, we need to find the values of f(x) for each given value of x. We can do this by plugging in the values of x into the function f(x) = -2x + 3.
x = -2
To find the value of f(-2), we plug in x = -2 into the function:
f(-2) = -2(-2) + 3 f(-2) = 4 + 3 f(-2) = 7
So, the value of f(-2) is 7.
x = -1
To find the value of f(-1), we plug in x = -1 into the function:
f(-1) = -2(-1) + 3 f(-1) = 2 + 3 f(-1) = 5
So, the value of f(-1) is 5.
x = 0
To find the value of f(0), we plug in x = 0 into the function:
f(0) = -2(0) + 3 f(0) = 0 + 3 f(0) = 3
So, the value of f(0) is 3.
x = 1
To find the value of f(1), we plug in x = 1 into the function:
f(1) = -2(1) + 3 f(1) = -2 + 3 f(1) = 1
So, the value of f(1) is 1.
x = 3
To find the value of f(3), we plug in x = 3 into the function:
f(3) = -2(3) + 3 f(3) = -6 + 3 f(3) = -3
So, the value of f(3) is -3.
In this article, we solved the function table for the given function f(x) = -2x + 3. We found the values of f(x) for each given value of x by plugging in the values into the function. The completed table is:
| x | f(x) |
|---|---|
| -2 | 7 |
| -1 | 5 |
| 0 | 3 |
| 1 | 1 |
| 3 | -3 |
We hope this article has helped you understand how to solve function tables for linear functions.
Frequently Asked Questions (FAQs) about Solving Function Tables
In our previous article, we solved the function table for the given function f(x) = -2x + 3. In this article, we will answer some frequently asked questions (FAQs) about solving function tables.
Q: What is a function table?
A: A function table is a table that shows the values of a function for different input values. It is a way to represent a function in a tabular form.
Q: How do I know if a function is linear or not?
A: A function is linear if it can be written in the slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept. If the function has a constant rate of change, it is a linear function.
Q: How do I find the values of f(x) for different values of x?
A: To find the values of f(x) for different values of x, you need to plug in the values of x into the function. For example, if the function is f(x) = -2x + 3, you would plug in x = 1, x = 2, x = 3, etc. into the function to find the corresponding values of f(x).
Q: What is the difference between a function table and a graph?
A: A function table is a table that shows the values of a function for different input values, while a graph is a visual representation of a function. A graph shows the relationship between the input values and the output values of a function.
Q: How do I use a function table to solve problems?
A: To use a function table to solve problems, you need to understand the relationship between the input values and the output values of the function. You can use the function table to find the values of f(x) for different values of x, and then use that information to solve problems.
Q: What are some common mistakes to avoid when solving function tables?
A: Some common mistakes to avoid when solving function tables include:
- Not understanding the relationship between the input values and the output values of the function
- Not plugging in the correct values of x into the function
- Not using the correct formula to find the values of f(x)
- Not checking the work for errors
Q: How do I check my work when solving function tables?
A: To check your work when solving function tables, you need to:
- Plug in the values of x into the function to find the corresponding values of f(x)
- Use the function table to find the values of f(x) for different values of x
- Check the work for errors by plugging in the values of x into the function and checking the results
In this article, we answered some frequently asked questions (FAQs) about solving function tables. We hope this article has helped you understand how to solve function tables and how to use them to solve problems.