Relations and Functions
More on Functions
| x | y |
| −7 | 0 |
| −2 | 5 |
| 2 | 9 |
| 6 | 13 |
The function above is represented by a table of values. It is also possible to represent it by describing the relationship between the corresponding values of x and y.
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Function Notation
The function given by the table above can be represented by the equation:
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By naming the function f, you can also use function notation to represent it: f(x) = x + 7.
The symbol f(x) is read “the value of f at x” or “f of x.” When given a function f, x is an input value and f(x) is an output value. Other letters can also be used to name functions, for example j(x)= 6x − 4 and h(x) =34x.
Determining if a Relation is a Function
A relation is a function if each input value is paired with only one output value. In this interactivity, you will determine if a relation is a function, whether it is represented by a table, a discrete graph, a set of ordered pairs, or a mapping. Also, you will learn how to use the vertical line test to determine if a relation represented by a continuous graph is a function. Click the player button to begin.
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Exploring Linear Functions
Prepare to explore the linear parent function f(x) = x by identifying the domain and range. As you work through the examples in this interactivity, you will discover how transformations of the parent function affect the domain and range. Click the player button to begin.
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Exploring Quadratic Functions
In this interactivity, you will explore the domain and range of the parent function of the quadratic function family, f(x) = x2. Can you predict how transformations of f(x) = x2 affect the domain and range? Click the player button to begin.
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Practical Problem
When a function is used to represent a practical situation, there may be restrictions placed on the domain. Consider the practical problem below.
Problem: The distance D that Anya’s car can be driven using g gallons of gas can be represented by the function D(g)=32g.
If the gas tank of Anya’s car holds a maximum of 12 gallons of gas, what is the domain of the function?
Response: Anya’s gas tank can hold a minimum of 0 gallons of gas and a maximum of 12 gallons of gas. Therefore the domain of the function is {x:0 ≤ x ≤ 12}.
Relations and Functions Review
Now that you have learned about relations and functions, it is time to test your knowledge. This interactivity will help you review the information covered throughout this topic. Click the player button to get started.
Did you answer the content review questions incorrectly? Do you want more instruction or extra practice? If so, view the videos Analyzing Relations and Functions and Analyzing the Quadratic Function Family from eMediaVASM.