Question

A function $f$ is a rule that assigns to each element $x$ in a set $A$ exactly $(i)$ element(s) called $f(x)$ in a set $B$. Which of the following tables defines $y$ as a function of $x ?$ $$\begin{array}{|c|c|} \hline x & y \\ \hline 1 & 5 \\ 2 & 7 \\ 3 & 6 \\ 4 & 8 \\ \hline \end{array}$$ $$\begin{array}{|c|c|} \hline x & y \\ \hline 1 & 5 \\ 1 & 7 \\ 2 & 6 \\ 3 & 8 \\ \hline \end{array}$$

Name: Problem 5, Chapter 2: College Algebra
Uploaded: 2020-08-21T20:46:27-08:00
Duration: 3 min 56 s
Channel: Ankit Gupta
Description: A function f is a rule that assigns to each element x in a set A exactly (i) element(s) called f(x) in a set B. Which of the following tables defines y as a function of x ? x y 1 5 2 7 3 6 4 8 x y 1 5 1 7 2 6 3 8

   A function $f$ is a rule that assigns to each element $x$ in a set $A$ exactly $(i)$ element(s) called $f(x)$ in a set $B$. Which of the following tables defines $y$ as a function of $x ?$
$$\begin{array}{|c|c|}
\hline x & y \\
\hline 1 & 5 \\
2 & 7 \\
3 & 6 \\
4 & 8 \\
\hline
\end{array}$$
$$\begin{array}{|c|c|}
\hline x & y \\
\hline 1 & 5 \\
1 & 7 \\
2 & 6 \\
3 & 8 \\
\hline
\end{array}$$

College Algebra

James Stewart,… 7th Edition

Chapter 2, Problem 5

Instant Answer

Solved by Expert Ankit Gupta

08/21/2020

Step 1

This means that for every input $x$ in set $A$, there is exactly one output $f(x)$ in set $B$. Show more…

Show all steps

Thanks for your feedback!

A function $f$ is a rule that assigns to each element $x$ in a set $A$ exactly $(i)$ element(s) called $f(x)$ in a set $B$. Which of the following tables defines $y$ as a function of $x ?$ $$\begin{array}{|c|c|} \hline x & y \\ \hline 1 & 5 \\ 2 & 7 \\ 3 & 6 \\ 4 & 8 \\ \hline \end{array}$$ $$\begin{array}{|c|c|} \hline x & y \\ \hline 1 & 5 \\ 1 & 7 \\ 2 & 6 \\ 3 & 8 \\ \hline \end{array}$$

Play audio

Feedback

Ankit Gupta and 96 other subject Algebra educators are ready to help you.

Ask a new question

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Function

A function is a mathematical rule that assigns every element in one set, called the domain, exactly one element in another set, called the codomain. This unique association distinguishes functions from more general relations.

Domain

The domain of a function is the set of all possible inputs. For a rule to be a function, each element in the domain must have an output, and no element is left without an assignment.

Unique Assignment

A key property of functions is that each input is associated with exactly one output. If an input corresponds to more than one output, then the rule does not qualify as a function.

Table Representation

When a function is represented in a table, each row typically shows a pairing of an input and its corresponding output. The table helps verify that each unique input is associated with only one output, confirming the definition of a function.

Please give Ace some feedback