Select The Correct Answer.Consider The Following Function: Y = 5 3 X + 2 Y=\frac{5}{3} X+2 Y = 3 5 X + 2 Using The Given Function, Select The Correct Set Of Ordered Pairs For The Following Domain Values: { − 12 , − 3 , 0 , 3 , 12 } \{-12,-3,0,3,12\} { − 12 , − 3 , 0 , 3 , 12 } A.

Mar 12, 2025 by ADMIN 283 views

**Selecting the Correct Ordered Pairs for a Given Function**

Understanding the Function

The given function is $y=\frac{5}{3} x+2$ . This is a linear function in the form of $y=mx+b$ , where $m$ is the slope and $b$ is the y-intercept. In this case, the slope is $\frac{5}{3}$ and the y-intercept is $2$ . To find the correct set of ordered pairs for the given domain values, we need to substitute each domain value into the function and solve for the corresponding y-value.

Substituting Domain Values into the Function

To find the correct set of ordered pairs, we need to substitute each domain value into the function and solve for the corresponding y-value. The domain values are $\{-12,-3,0,3,12\}$ . We will substitute each value into the function and calculate the corresponding y-value.

Substituting -12 into the Function

To find the y-value corresponding to the domain value $-12$ , we substitute $-12$ into the function:

y=\frac{5}{3}(-12)+2

Simplifying the expression, we get:

y=-20+2

y=-18

So, the ordered pair corresponding to the domain value $-12$ is $(-12,-18)$ .

Substituting -3 into the Function

To find the y-value corresponding to the domain value $-3$ , we substitute $-3$ into the function:

y=\frac{5}{3}(-3)+2

Simplifying the expression, we get:

y=-5+2

y=-3

So, the ordered pair corresponding to the domain value $-3$ is $(-3,-3)$ .

Substituting 0 into the Function

To find the y-value corresponding to the domain value $0$ , we substitute $0$ into the function:

y=\frac{5}{3}(0)+2

Simplifying the expression, we get:

y=0+2

y=2

So, the ordered pair corresponding to the domain value $0$ is $(0,2)$ .

Substituting 3 into the Function

To find the y-value corresponding to the domain value $3$ , we substitute $3$ into the function:

y=\frac{5}{3}(3)+2

Simplifying the expression, we get:

y=5+2

y=7

So, the ordered pair corresponding to the domain value $3$ is $(3,7)$ .

Substituting 12 into the Function

To find the y-value corresponding to the domain value $12$ , we substitute $12$ into the function:

y=\frac{5}{3}(12)+2

Simplifying the expression, we get:

y=20+2

y=22

So, the ordered pair corresponding to the domain value $12$ is $(12,22)$ .

Selecting the Correct Set of Ordered Pairs

Based on the calculations above, the correct set of ordered pairs for the given domain values is:

$(-12,-18),(-3,-3),(0,2),(3,7),(12,22)$

This set of ordered pairs represents the points on the graph of the function $y=\frac{5}{3} x+2$ for the given domain values.

Conclusion

In this article, we have discussed how to select the correct set of ordered pairs for a given function. We have used the function $y=\frac{5}{3} x+2$ and the domain values $\{-12,-3,0,3,12\}$ to illustrate the process. By substituting each domain value into the function and solving for the corresponding y-value, we have found the correct set of ordered pairs. This set of ordered pairs represents the points on the graph of the function for the given domain values.

Q: What is the purpose of selecting the correct ordered pairs for a given function?

A: The purpose of selecting the correct ordered pairs for a given function is to find the points on the graph of the function for a specific set of domain values. This is useful in various applications, such as graphing functions, solving equations, and analyzing data.

Q: How do I select the correct ordered pairs for a given function?

A: To select the correct ordered pairs for a given function, you need to substitute each domain value into the function and solve for the corresponding y-value. This involves using the function equation and the given domain values to find the points on the graph of the function.

Q: What is the difference between a domain value and a range value?

A: A domain value is the input value in a function, while a range value is the output value. In other words, the domain value is the x-value, and the range value is the y-value.

Q: How do I know if I have selected the correct ordered pairs for a given function?

A: To ensure that you have selected the correct ordered pairs for a given function, you need to check your work by plugging the ordered pairs back into the function equation. If the equation holds true, then you have selected the correct ordered pairs.

Q: Can I use a calculator to select the correct ordered pairs for a given function?

A: Yes, you can use a calculator to select the correct ordered pairs for a given function. However, it is always a good idea to double-check your work by plugging the ordered pairs back into the function equation to ensure accuracy.

Q: What if I make a mistake when selecting the correct ordered pairs for a given function?

A: If you make a mistake when selecting the correct ordered pairs for a given function, you can try re-substituting the domain values into the function equation or re-checking your work to ensure accuracy.

Q: Can I use the correct ordered pairs for a given function to solve equations?

A: Yes, you can use the correct ordered pairs for a given function to solve equations. By substituting the ordered pairs into the equation, you can solve for the unknown variable.

Q: Can I use the correct ordered pairs for a given function to graph the function?

A: Yes, you can use the correct ordered pairs for a given function to graph the function. By plotting the ordered pairs on a coordinate plane, you can visualize the graph of the function.

Q: What are some common mistakes to avoid when selecting the correct ordered pairs for a given function?

A: Some common mistakes to avoid when selecting the correct ordered pairs for a given function include:

Not substituting the domain values into the function equation correctly
Not solving for the corresponding y-value correctly
Not checking the work by plugging the ordered pairs back into the function equation
Not using the correct function equation

Q: How can I practice selecting the correct ordered pairs for a given function?

A: You can practice selecting the correct ordered pairs for a given function by working through examples and exercises in a textbook or online resource. You can also try creating your own examples and exercises to practice selecting the correct ordered pairs for a given function.

Q: What are some real-world applications of selecting the correct ordered pairs for a given function?

A: Some real-world applications of selecting the correct ordered pairs for a given function include:

Graphing functions to model real-world situations
Solving equations to find unknown values
Analyzing data to make informed decisions
Creating mathematical models to predict outcomes

Conclusion

In this article, we have discussed frequently asked questions about selecting the correct ordered pairs for a given function. We have covered topics such as the purpose of selecting the correct ordered pairs, how to select the correct ordered pairs, and common mistakes to avoid. We have also discussed real-world applications of selecting the correct ordered pairs for a given function. By understanding these concepts, you can become more confident and proficient in selecting the correct ordered pairs for a given function.