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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

For each graph, determine whether y is a function of x. Give the domain and range of each relation.
Graph showing two relations on an xy-plane with arrows, illustrating function determination and domain-range analysis.

Verified step by step guidance
1
Step 1: Identify if y is a function of x by using the vertical line test. A relation is a function if every vertical line intersects the graph at most once.
Step 2: Observe the graph carefully. Notice that at x = 0, there are two different y-values: y = 2 (solid point) and y = 4 (open circle). This means a vertical line at x = 0 intersects the graph twice.
Step 3: Since the vertical line at x = 0 intersects the graph more than once, y is not a function of x for this relation.
Step 4: Determine the domain by looking at the x-values covered by the graph. The graph extends from about x = -20 to x = 20, so the domain is approximately \([-20, 20]\).
Step 5: Determine the range by looking at the y-values covered by the graph. The lowest y-value is about 2 (solid point at x=0), and the graph extends upward beyond y = 10, so the range is approximately \([2, \infty)\).

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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 (x-value) corresponds to exactly one output (y-value). This means no vertical line intersects the graph at more than one point, ensuring each x has a unique y.
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Domain and Range

The domain is the set of all possible x-values for which the function or relation is defined. The range is the set of all possible y-values that the function or relation can take. Identifying these helps describe the extent of the graph.
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Vertical Line Test

The vertical line test is a visual way to determine if a graph represents a function. If any vertical line crosses the graph more than once, the graph does not represent a function because an x-value maps to multiple y-values.
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Related Practice
Textbook Question

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

ƒ(x)=√(4x-1), g(x)=1/x

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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)=√(4x-1), g(x)=1/x

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Textbook Question

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

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 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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Textbook Question

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

ƒ(x)=√(4x-1), g(x)=1/x

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