Representation using an equation of and
Representation using an equation of and
Representation using a graph, plotting on the and axis
Representation using a table of points on the graph
Expressing the relationship between and using words
or
Is the given graph a function?
Before we talk about algebraic representation, it is important to understand what a function means.
A function describes the relationship between and .
In any function, is the independent variable and is the dependent variable. This means that every time we change , we get a different .
Y depends on and depends on nothing.
Important point: For each there will be only one !
An algebraic representation of a function is essentially the equation of the function.
Let's look at some examples of algebraic representation of a function and analyze them:
In this equation, it is clear that depends on the we substitute into the equation.
If , then
If , then
If , then
In other words, the relationship between and is that will always be less than .
Now let's examine another equation:
Also in this equation, it is clear that depends on the we substitute into the equation.
If , then
If , then
If , then
In this equation, it is difficult to define in words the relationship between and , so we will say that the relationship between them is the equation itself:
Now let's examine another equation:
In this equation, it is also clear that depends on the we substitute into the equation.
If , then
If , then
If , then
The relationship between and is that they are identical each time.
Click here to learn more about the algebraic representation of a function!
A graphical representation of a function shows us how the function looks on the and axes.
What is most important to know?
For each , there is only one , and to draw a function as a graph, it is advisable to find at least 3 points of the function.
How to draw the function:
Each time, substitute a different into the algebraic representation and identify its . Mark all the points obtained on the drawing and then draw a straight line between them.
For example:
Let's substitute three s and we get:
0 | -2 |
2 |
Now let's mark the points we obtained on the number line:
Examples of graphical representation of a function:
Important tips:
How do you know if the function is increasing or decreasing?
There are 2 ways:
You can read more about the graphical representation of a function at this link!
Is the given graph a function?
Is the given graph a function?
Determine whether the following table represents a function
A tabular representation is essentially a representation using a table of and showing us the value of for each that we substitute into the function.
Let's see an example:
For the algebraic representation -
we get a tabular representation like this:
A verbal representation of a function describes the relationship between and using words.
For example:
Each package of flour () makes whole pizzas ()
For more information on verbal and tabular representation of a function, click here!
Determine whether the following table represents a function
Determine whether the data in the following table represent a constant function
Determine whether the following table represents a function
How do we denote a function?
So far, we have denoted a function as
It is also useful to know that a function can be denoted in the following way:
which implies that we will get a value that depends on .
You can read more about function notation here!
Determine whether the following table represents a function
Is the given graph a function?
Is the given graph a function?
Which of the following equations corresponds to the function represented in the graph?
Use the formula for finding slope:
We take the points:
We substitute the point and slope into the line equation:
We combine like terms:
Therefore, the equation will be:
Which of the following equations corresponds to the function represented in the table?
We will use the formula for finding slope:
Let's take the points:
We'll substitute the point and slope into the line equation:
Let's combine like terms:
Therefore, the equation will be:
Is the given graph a function?
Yes
Is the given graph a function?
No
Is the given graph a function?
Yes