Answered: Use the given graph of f to state the…

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter5: Linear Inequalities

Section5.2: Solving Inequalities By Multiplication And Division

Problem 3AGP

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Question

Use the given graph of f to state the value of each quantity, if it exists. (If an answer does not exist, enter DNE.)

Expert Solution

Step 1: Introduce to the given graph

The graph of the function f(x) is shown as,

Step 2: Define the limit

Limit of function f(x) at x=a,

$For space straight a space function space f left parenthesis x right parenthesis comma limit as x rightwards arrow a of f open parentheses x close parentheses space exists space if space and space only space if space limit as x rightwards arrow a to the power of minus of f open parentheses x close parentheses equals limit as x rightwards arrow a to the power of plus of f open parentheses x close parentheses equals L then limit as x rightwards arrow a of f open parentheses x close parentheses equals L$

And,

$limit as x rightwards arrow a of f open parentheses x close parentheses$ - this represents the value function approaches when x approaches to a.

$f open parentheses a close parentheses$ - this represents the value of function at x=a.

Step 3: Determine the limits and value of function at x=2

Part-(a)

From the graph,

it can be observed that the function approaches to value 3 when x approaches to 2 from left hand side.

$limit as x rightwards arrow 2 to the power of minus of f open parentheses x close parentheses equals the space value space function space aaproaches space when space straight x space approaches space to space 2 space from space left space hand space side limit as straight x rightwards arrow 2 to the power of minus of straight f open parentheses straight x close parentheses equals 3$

Part-(b)

From the graph,

it can be observed that the function approaches to value 1 when x approaches to 2 from right hand side.

$limit as x rightwards arrow 2 to the power of plus of f open parentheses x close parentheses equals the space value space function space aaproaches space when space straight x space approaches space to space 2 space from space right space hand space side limit as straight x rightwards arrow 2 to the power of plus of straight f open parentheses straight x close parentheses equals 1$ F

Part-(c)

From part a and b,

$limit as x rightwards arrow 2 to the power of minus of f open parentheses x close parentheses equals 3 limit as x rightwards arrow 2 to the power of plus of f open parentheses x close parentheses equals 1 rightwards double arrow limit as x rightwards arrow 2 to the power of minus of f open parentheses x close parentheses not equal to limit as x rightwards arrow 2 to the power of plus of f open parentheses x close parentheses So comma limit as x rightwards arrow 2 of f open parentheses x close parentheses space does space not space exist.$

Part-(d)

A solid point represents that the value of the function at that specific point is included.

From the graph,

$f open parentheses 2 close parentheses$ = value of function at x=2

$f open parentheses 2 close parentheses equals 3$

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