Function, describes a correlation or coincidence between a dependent variable () and an independent variable (). The legitimacy of this relationship between the variables is called the " correspondence rule ".
Representing a Function Verbally and with Tables - Examples, Exercises and Solutions
Understanding Representing a Function Verbally and with Tables
Complete explanation with examples
Verbal representation of a function
The verbal representation of a function expresses the connection between variables verbally, i.e. through a story.
A typical verbal representation of a function can look like this:
- Assuming that Daniel reads all the books he buys that month, the total number of books Daniel reads per year () is a function of the number of books Danny buys each month ().
Tabular representation of a function
A tabular representation of a function is a demonstration of the legitimacy of a function using a table of values (independent variable) and the corresponding values (dependent variable).
In general, a table of values is shown as follows:
Practice Representing a Function Verbally and with Tables
Test your knowledge with 12 quizzes
Which of the following equations corresponds to the function represented in the graph?
Examples with solutions for Representing a Function Verbally and with Tables
Step-by-step solutions included
Exercise #1
Determine whether the following table represents a function
Step-by-Step Solution
It is important to remember that a constant function describes a situation where as the X value increases, the function value (Y) remains constant.
In the table, we can observe that there is a constant change in X values, meaning an increase of 1, and a constant change in Y values, meaning an increase of 3
Therefore, according to the rule, the table describes a function.
Answer:
Yes
Video Solution
Exercise #2
Determine whether the data in the following table represent a constant function
Step-by-Step Solution
It is important to remember that a constant function describes a situation where as the X value increases, the function value (Y) remains constant.
In the table, we can observe that there is a constant change in X values, meaning an increase of 1, and a non-constant change in Y values - sometimes increasing by 1 and sometimes by 4
Therefore, according to the rule, the table does not describe a function
Answer:
No
Video Solution
Exercise #3
Determine whether the following table represents a constant function:
Step-by-Step Solution
It is important to remember that a constant function describes a situation where, as the X value increases, the Y value remains constant.
In the table, we can see that there is a constant change in the X values, specifically an increase of 2, while the Y value remains constant.
Therefore, the table does indeed describe a constant function.
Answer:
Yes, it does
Video Solution
Exercise #4
Is the given graph a function?
Step-by-Step Solution
It is important to remember that a function is an equation that assigns to each element in domain X one and only one element in range Y
Let's note that in the graph:
In other words, there are two values for the same number.
Therefore, the graph is not a function.
Answer:
No
Video Solution
Exercise #5
Determine whether the given graph is a function?
Step-by-Step Solution
It is important to remember that a function is an equation that assigns to each element in domain X one and only one element in range Y
We should note that for every X value found on the graph, there is one and only one corresponding Y value.
Therefore, the graph is indeed a function.
Answer:
Yes
Video Solution