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Ch. 2 - Graphs and Functions
Lial - College Algebra 13th Edition
Lial13th EditionCollege AlgebraISBN: 9780136881063Not the one you use?Change textbook
All textbooksLial 13th EditionCh. 2 - Graphs and FunctionsProblem 24
Chapter 3, Problem 24

Determine whether each relation defines a function, and give the domain and range.

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1
Understand the definition of a function: A relation is a function if every input (or domain value) corresponds to exactly one output (or range value).
Identify the domain of the relation by listing all the input values (usually the x-values) from the given set or description.
Check each input value to see if it is paired with only one output value. If any input has more than one output, the relation is not a function.
If the relation is a function, determine the range by listing all the output values (usually the y-values) that correspond to the inputs in the domain.
Summarize your findings by stating whether the relation is a function, and clearly specify the domain and range using set notation or interval notation as appropriate.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Definition of a Function

A function is a relation where each input (domain element) corresponds to exactly one output (range element). This means no input value can be paired with more than one output value. Understanding this helps determine if a given relation qualifies as a function.
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Domain of a Relation

The domain is the set of all possible input values (usually x-values) in a relation. Identifying the domain involves listing all unique first elements from the ordered pairs or the input values for which the relation is defined.
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Range of a Relation

The range is the set of all possible output values (usually y-values) in a relation. To find the range, list all unique second elements from the ordered pairs or the outputs that correspond to the inputs in the domain.
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Related Practice
Textbook Question

For the pair of functions defined, find (ƒ+g)(x), (ƒ-g)(x), (ƒg)(x), and (f/g)(x).Give the domain of each. ƒ(x)=√(5x-4), g(x)=-(1/x)

Textbook Question

Determine whether the three points are the vertices of a right triangle. (-4,1),(1,4),(-6,-1)

Textbook Question

Determine whether the three points are the vertices of a right triangle. See Example 3.

(−2,−8),(0,−4),(−4,−7)(-2,-8),(0,-4),(-4,-7)

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Textbook Question

Graph each function. See Examples 1 and 2. ƒ(x)=-(1/2)x2

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Textbook Question

For each graph, determine whether y is a function of x. Give the domain and range of each relation.

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Textbook Question

Graph each piecewise-defined function.

f(x)={2x+1if x≥0xif x<0f(x) =\(\begin{cases}\)2x + 1 & \(\text{if }\) x \(\geq\) 0 \(\x\) & \(\text{if }\) x < 0\(\end{cases}\)

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