As we learned in an article on functions, the standard "correspondence rule" is a connection between a dependent variable (Y) and an independent variable (X).
By means of a graph or drawing, which gives a visual aspect to the concept of the function. From the graph it is possible to understand whether it is a linear function (straight line), a quadratic function (parabola) and more.
Remember that when it comes to a graphical representation of a function, each point in the domain X will always have only one point within the range Y. Therefore, not every drawing is a graphical representation of a function. Here is an example.
As we know a function can be represented in different ways: verbally, algebraically, table of values and graphically. The last representation means that a function can be graphed in the Cartesian plane, according to the values obtained in the table, this representation can be observed as a straight line, a parabola, among others, depending on the type of function we are working on.
How is a function represented graphically?
Let's see an example of how a function should be represented graphically.
Example:
Represent the following function in a graph
Task
Graph the following function Y=X−1
Solution
We are going to give values to X, to find the value of Y, according to the correspondence rule, and we are going to register these values in a table:
First, we are going to input the values of X To get the values that correspond to Y, the algebraic expression of this function is:
Y=X−1
Then,
When X=−4
Y=−4−1=−5
When X=−3
Y=−3−1=−4
When X=−1
Y=−1−1=−2
When When X=0
Y=0−1=−1
When X=2
Y=2−1=1
When X=5
Y=5−1=4
According to this data now we are going to input it in the table
Once we have the values in the table, we are going to look for these pairs of coordinates in the Cartesian plane, where we are going to find points and connect them as follows to obtain the final graph of the function
Graph:
According to these points that were located in the Cartesian plane, we can observe that a straight line was drawn, which means that the function is linear.
What are the types of graphical representation of a function?
There are many graphs of functions, this is according to the type of function that is being graphed, among the most common are:
Graph of a constant function
Graph of a linear function
Graph of a quadratic function
Graph of a cubic function
Graph of an exponential function
Do you think you will be able to solve it?
Question 1
Determine whether the following table represents a function
Examples with solutions for Graphical Representation of a Function
Exercise #1
Is the given graph a function?
Video Solution
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
Exercise #2
Is the given graph a function?
Video Solution
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:
f(0)=2,f(0)=−2
In other words, there are two values for the same number.
Therefore, the graph is not a function.
Answer
No
Exercise #3
Is the given graph a function?
Video Solution
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 in the graph, there is one and only one corresponding Y value.
Therefore, the graph is indeed a function.
Answer
Yes
Exercise #4
Determine whether the following table represents a function
Video Solution
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 see 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
Exercise #5
Determine whether the following table represents a function
Video Solution
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 see that there is a constant change in the X values, specifically an increase of 2, and the Y value remains constant.
Therefore, according to the rule, the table describes a constant function.
