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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 22
Chapter 3, Problem 22

Determine whether each relation defines a function, and give the domain and range.
Diagram showing arrows from set {1, 2, 3, 5} to {10, 15, 19, 27} illustrating a relation.

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Step 1: Identify the domain and range from the diagram. The domain consists of all the input values on the left side, which are 4, 9, 13, and 19. The range consists of all the output values on the right side, which are 18, 25, 28, and 35.
Step 2: Determine if the relation defines a function. Recall that a relation is a function if each input (domain value) corresponds to exactly one output (range value). Check if any input value maps to more than one output.
Step 3: Observe the arrows in the diagram. Each input value (4, 9, 13, 19) points to exactly one output value (18, 25, 28, 35) respectively, with no input having multiple outputs.
Step 4: Conclude that since each input has exactly one output, the relation is a function.
Step 5: Summarize the domain and range: Domain = {4, 9, 13, 19} and Range = {18, 25, 28, 35}.

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Key Concepts

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

Relation and Function

A relation is a set of ordered pairs connecting elements from one set (domain) to another (range). A function is a special type of relation where each input in the domain maps to exactly one output in the range. This means no input can correspond to multiple outputs.
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Domain

The domain of a relation or function is the set of all possible input values. In the given diagram, the domain consists of the numbers on the left side (4, 9, 13, 19), representing all inputs that are related to outputs.
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Range

The range is the set of all possible output values that correspond to the inputs in the domain. In the diagram, the range includes the numbers on the right side (18, 25, 28, 35), which are the outputs related to the inputs.
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Related Practice
Textbook Question

Graph each piecewise-defined function.

f(x)={6−xif x≤33if x>3f(x) =\(\begin{cases}\)6 - x & \(\text{if }\) x \(\leq\) 3 \\3 & \(\text{if }\) x > 3\(\end{cases}\)

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Textbook Question

Graph each function. See Examples 1 and 2. g(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

For the pair of functions defined, find (ƒ/g)(x). Give the domain of each. See Example 2.

ƒ(x)=2x^2-3x, g(x)=x^2-x+3

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Textbook Question

For the pair of functions defined, find (ƒg)(x). Give the domain of each. See Example 2.

ƒ(x)=2x^2-3x, g(x)=x^2-x+3

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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)=4x2+2x, g(x)=x2-3x+2

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