Westonci.ca is your go-to source for answers, with a community ready to provide accurate and timely information. Discover in-depth solutions to your questions from a wide range of experts on our user-friendly Q&A platform. Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals.

Question 4 of 25

Does this set of ordered pairs represent a function? Why or why not?

[tex]\[
\{(-5, -5), (-1, -2), (0, -2), (3, 7), (8, 9)\}
\][/tex]

A. Yes, because there are two [tex]$x$[/tex]-values that are the same.
B. No, because one [tex]$x$[/tex]-value corresponds to two different [tex]$y$[/tex]-values.
C. Yes, because every [tex]$x$[/tex]-value corresponds to exactly one [tex]$y$[/tex]-value.
D. No, because two of the [tex]$y$[/tex]-values are the same.


Sagot :

To determine whether the given set of ordered pairs represents a function, we need to evaluate whether each unique \( x \)-value corresponds to exactly one unique \( y \)-value. In other words, an \( x \)-value should not map to multiple \( y \)-values for the set to be a function.

Given the set of ordered pairs:
[tex]\[ \{(-5, -5), (-1, -2), (0, -2), (3, 7), (8, 9)\} \][/tex]

Let's examine the \( x \)-values and their corresponding \( y \)-values:

1. For \( x = -5 \), \( y = -5 \)
2. For \( x = -1 \), \( y = -2 \)
3. For \( x = 0 \), \( y = -2 \)
4. For \( x = 3 \), \( y = 7 \)
5. For \( x = 8 \), \( y = 9 \)

We observe the following:
- Each \( x \)-value in the set is unique.
- No \( x \)-value is repeated with a different \( y \)-value.

Since every \( x \)-value in the set corresponds to exactly one \( y \)-value, this set of ordered pairs represents a function.

Hence, the answer is:

C. Yes, because every [tex]\( x \)[/tex]-value corresponds to exactly one [tex]\( y \)[/tex]-value.
Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Keep exploring Westonci.ca for more insightful answers to your questions. We're here to help.