(a) Answer The domain of function is all the real numbers except x = 0 . Explanation Given information: The function is f ( x ) = 1 − x 2 x Calculation: Consider the function. . f ( x ) = 1 − x 2 x The function is valid for all the real numbers except x = 0 as the denominator becomes zero and the function is undefined for this value. Therefore, the domain of function is all the real numbers except x = 0 (b) To determine To find: The intercepts. Answer The y- intercept is absent and the x- intercept is ( 0 , 1 ) and ( 0 , − 1 ) . Explanation Given information: The function is f ( x ) = 1 − x 2 x Calculation: The y intercept is absent as the function becomes undefined. Equate function to zero to find x intercept. f ( 0 ) = 0 1 − x 2 x = 0 x 2 = 1 x = ± 1 Therefore, the y- intercept is absent and the x- intercept is ( 0 , 1 ) and ( 0 , − 1 ) . (c) To determine To find: The asymptotes. Answer The slant asymptote is y = − x . Explanation Given information: The function is f ( x ) = 1 − x 2 x Calculation: In given function degree of numerator is one more than the degree of denominator. The graph will have slant asymptote which can be calculated by dividing numerator wuth denominator. f ( x ) = − x + 1 x Here the slant asymptote will be y = − x as 1 x becomes zero when x becomes infinite. Therefore, the slant asymptote is y = − x . (d) To determine To find: The sketch of graph. Answer The graph is shown in Figure-(1). Explanation Given information: The function is f ( x ) = 1 − x 2 x Calculation: The below table shows additional points Test Interval Value of x Value of f Sign Point of f ( − ∞ , − 1 ) -2 3 2 Positive ( − 2 , 3 2 ) ( − , 0 ) − 1 2 − 3 2 Negative ( − 1 2 , − 3 2 ) ( 0 , 1 ) 1 2 3 2 Positive ( 1 2 , 3 2 ) ( 1 , ∞ ) 2 − 3 2 Negative ( 2 , − 3 2 ) Draw the sketch for the function by using the equations of asymptotes. Figure-(1) Therefore, the graph is shown in Figure-(1).

3rd Edition

ISBN: 9781133947202

Author: Ron Larson

Publisher: Cengage Learning

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Question

Chapter 2.6, Problem 52E

(a)

To determine

To find:The domain of function.

(a)

Expert Solution

Answer to Problem 52E

The domain of function is all the real numbers except $x=0$ .

Explanation of Solution

Given information:

The function is $f(x)=1−x2x$

Calculation:

Consider the function.

. $f(x)=1−x2x$

The function is valid for all the real numbers except $x=0$ as the denominator becomes zero and the function is undefined for this value.

Therefore, the domain of function is all the real numbers except $x=0$

(b)

To determine

To find:The intercepts.

(b)

Expert Solution

Answer to Problem 52E

The y- intercept is absent and the x- intercept is $(0,1)$ and $(0,−1)$ .

Explanation of Solution

Given information:

The function is $f(x)=1−x2x$

Calculation:

The y intercept is absent as the function becomes undefined.

Equate function to zero to find x intercept.

$f(0)=01−x2x=0x2=1x=±1$

Therefore, the y- intercept is absent and the x- intercept is $(0,1)$ and $(0,−1)$ .

(c)

To determine

To find:The asymptotes.

(c)

Expert Solution

Answer to Problem 52E

The slant asymptote is $y=−x$ .

Explanation of Solution

Given information:

The function is $f(x)=1−x2x$

Calculation:

In given function degree of numerator is one more than the degree of denominator. The graph will have slant asymptote which can be calculated by dividing numerator wuth denominator.

$f(x)=−x+1x$

Here the slant asymptote will be $y=−x$ as $1x$ becomes zero when x becomes infinite.

Therefore, the slant asymptote is $y=−x$ .

(d)

To determine

To find:The sketch of graph.

(d)

Expert Solution

Answer to Problem 52E

The graph is shown in Figure-(1).

Explanation of Solution

Given information:

The function is $f(x)=1−x2x$

Calculation:

The below table shows additional points

Test Interval	Value of x	Value of f	Sign	Point of f
$(−∞,−1)$	-2	$32$	Positive	$(−2,32)$
$(−,0)$	$−12$	$−32$	Negative	$(−12,−32)$
$(0,1)$	$12$	$32$	Positive	$(12,32)$
$(1,∞)$	2	$−32$	Negative	$(2,−32)$

Draw the sketch for the function by using the equations of asymptotes.

Precalculus with Limits, Chapter 2.6, Problem 52E

Figure-(1)

Therefore, the graph is shown in Figure-(1).

Chapter 2.6, Problem 51E

Chapter 2.6, Problem 53E

Chapter 2 Solutions

Precalculus with Limits

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Prob. 23E Ch. 2.6 - Prob. 24E Ch. 2.6 - Prob. 25E Ch. 2.6 - Prob. 26E Ch. 2.6 - Prob. 27E Ch. 2.6 - Prob. 28E Ch. 2.6 - Prob. 29E Ch. 2.6 - Prob. 30E Ch. 2.6 - Prob. 31E Ch. 2.6 - Prob. 32E Ch. 2.6 - Prob. 33E Ch. 2.6 - Prob. 34E Ch. 2.6 - Prob. 35E Ch. 2.6 - Prob. 36E Ch. 2.6 - Prob. 37E Ch. 2.6 - Prob. 38E Ch. 2.6 - Prob. 39E Ch. 2.6 - Prob. 40E Ch. 2.6 - Prob. 41E Ch. 2.6 - Prob. 42E Ch. 2.6 - Prob. 43E Ch. 2.6 - Prob. 44E Ch. 2.6 - Prob. 45E Ch. 2.6 - Prob. 46E Ch. 2.6 - Prob. 47E Ch. 2.6 - Prob. 48E Ch. 2.6 - Prob. 49E Ch. 2.6 - Prob. 50E Ch. 2.6 - Prob. 51E Ch. 2.6 - Prob. 52E Ch. 2.6 - Prob. 53E Ch. 2.6 - Prob. 54E Ch. 2.6 - Prob. 55E Ch. 2.6 - Prob. 56E Ch. 2.6 - Prob. 57E Ch. 2.6 - Prob. 58E Ch. 2.6 - Prob. 59E Ch. 2.6 - Prob. 60E Ch. 2.6 - Prob. 61E Ch. 2.6 - Prob. 62E Ch. 2.6 - Prob. 63E Ch. 2.6 - Prob. 64E Ch. 2.6 - Prob. 65E Ch. 2.6 - Prob. 66E Ch. 2.6 - Prob. 67E Ch. 2.6 - Prob. 68E Ch. 2.6 - Prob. 69E Ch. 2.6 - Prob. 70E Ch. 2.6 - Prob. 71E Ch. 2.6 - Prob. 72E Ch. 2.6 - Prob. 73E Ch. 2.6 - Prob. 74E Ch. 2.6 - Prob. 75E Ch. 2.6 - Prob. 76E Ch. 2.6 - Prob. 77E Ch. 2.6 - Prob. 78E Ch. 2.6 - Prob. 79E Ch. 2.6 - Prob. 80E Ch. 2.6 - Prob. 81E Ch. 2.6 - Prob. 82E Ch. 2.7 - Prob. 1E Ch. 2.7 - Prob. 2E Ch. 2.7 - Prob. 3E Ch. 2.7 - Prob. 4E Ch. 2.7 - Prob. 5E Ch. 2.7 - Prob. 6E Ch. 2.7 - Prob. 7E Ch. 2.7 - Prob. 8E Ch. 2.7 - Prob. 9E Ch. 2.7 - Prob. 10E Ch. 2.7 - Prob. 11E Ch. 2.7 - Prob. 12E Ch. 2.7 - Prob. 13E Ch. 2.7 - Prob. 14E Ch. 2.7 - Prob. 15E Ch. 2.7 - Prob. 16E Ch. 2.7 - Prob. 17E Ch. 2.7 - Prob. 18E Ch. 2.7 - Prob. 19E Ch. 2.7 - Prob. 20E Ch. 2.7 - Prob. 21E Ch. 2.7 - Prob. 22E Ch. 2.7 - Prob. 23E Ch. 2.7 - Prob. 24E Ch. 2.7 - Prob. 25E Ch. 2.7 - Prob. 26E Ch. 2.7 - Prob. 27E Ch. 2.7 - Prob. 28E Ch. 2.7 - Prob. 29E Ch. 2.7 - Prob. 30E Ch. 2.7 - Prob. 31E Ch. 2.7 - Prob. 32E Ch. 2.7 - Prob. 33E Ch. 2.7 - Prob. 34E Ch. 2.7 - Prob. 35E Ch. 2.7 - Prob. 36E Ch. 2.7 - Prob. 37E Ch. 2.7 - Prob. 38E Ch. 2.7 - Prob. 39E Ch. 2.7 - Prob. 40E Ch. 2.7 - Prob. 41E Ch. 2.7 - Prob. 42E Ch. 2.7 - Prob. 43E Ch. 2.7 - Prob. 44E Ch. 2.7 - Prob. 45E Ch. 2.7 - Prob. 46E Ch. 2.7 - Prob. 47E Ch. 2.7 - Prob. 48E Ch. 2.7 - Prob. 49E Ch. 2.7 - Prob. 50E Ch. 2.7 - Prob. 51E Ch. 2.7 - Prob. 52E Ch. 2.7 - Prob. 53E Ch. 2.7 - Prob. 54E Ch. 2.7 - Prob. 55E Ch. 2.7 - Prob. 56E Ch. 2.7 - Prob. 57E Ch. 2.7 - Prob. 58E Ch. 2.7 - Prob. 59E Ch. 2.7 - Prob. 60E Ch. 2.7 - Prob. 61E Ch. 2.7 - Prob. 62E Ch. 2.7 - Prob. 63E Ch. 2.7 - Prob. 64E Ch. 2.7 - Prob. 65E Ch. 2.7 - Prob. 66E Ch. 2.7 - Prob. 67E Ch. 2.7 - Prob. 68E Ch. 2.7 - Prob. 69E Ch. 2.7 - Prob. 70E Ch. 2.7 - Prob. 71E Ch. 2.7 - Prob. 72E Ch. 2.7 - Prob. 73E Ch. 2.7 - Prob. 74E Ch. 2.7 - Prob. 75E Ch. 2.7 - Prob. 76E Ch. 2.7 - Prob. 77E Ch. 2.7 - Prob. 78E Ch. 2.7 - Prob. 79E Ch. 2.7 - Prob. 80E Ch. 2.7 - Prob. 81E Ch. 2.7 - Prob. 82E Ch. 2.7 - Prob. 83E Ch. 2.7 - Prob. 84E Ch. 2.7 - Prob. 85E Ch. 2.7 - Prob. 86E Ch. 2.7 - Prob. 87E Ch. 2.7 - Prob. 88E Ch. 2.7 - Prob. 89E Ch. 2.7 - Prob. 90E Ch. 2 - Prob. 1RE Ch. 2 - Prob. 2RE Ch. 2 - Prob. 3RE Ch. 2 - Prob. 4RE Ch. 2 - Prob. 5RE Ch. 2 - Prob. 6RE Ch. 2 - Prob. 7RE Ch. 2 - Prob. 8RE Ch. 2 - Prob. 9RE Ch. 2 - Prob. 10RE Ch. 2 - Prob. 11RE Ch. 2 - Prob. 12RE Ch. 2 - Prob. 13RE Ch. 2 - Prob. 14RE Ch. 2 - Prob. 15RE Ch. 2 - Prob. 16RE Ch. 2 - Prob. 17RE Ch. 2 - Prob. 18RE Ch. 2 - Prob. 19RE Ch. 2 - Prob. 20RE Ch. 2 - Prob. 21RE Ch. 2 - Prob. 22RE Ch. 2 - Prob. 23RE Ch. 2 - Prob. 24RE Ch. 2 - Prob. 25RE Ch. 2 - Prob. 26RE Ch. 2 - Prob. 27RE Ch. 2 - Prob. 28RE Ch. 2 - Prob. 29RE Ch. 2 - Prob. 30RE Ch. 2 - Prob. 31RE Ch. 2 - Prob. 32RE Ch. 2 - Prob. 33RE Ch. 2 - Prob. 34RE Ch. 2 - Prob. 35RE Ch. 2 - Prob. 36RE Ch. 2 - Prob. 37RE Ch. 2 - Prob. 38RE Ch. 2 - Prob. 39RE Ch. 2 - Prob. 40RE Ch. 2 - Prob. 41RE Ch. 2 - Prob. 42RE Ch. 2 - Prob. 43RE Ch. 2 - Prob. 44RE Ch. 2 - Prob. 45RE Ch. 2 - Prob. 46RE Ch. 2 - Prob. 47RE Ch. 2 - Prob. 48RE Ch. 2 - Prob. 49RE Ch. 2 - Prob. 50RE Ch. 2 - Prob. 51RE Ch. 2 - Prob. 52RE Ch. 2 - Prob. 53RE Ch. 2 - Prob. 54RE Ch. 2 - Prob. 55RE Ch. 2 - Prob. 56RE Ch. 2 - Prob. 57RE Ch. 2 - Prob. 58RE Ch. 2 - Prob. 59RE Ch. 2 - Prob. 60RE Ch. 2 - Prob. 61RE Ch. 2 - Prob. 62RE Ch. 2 - Prob. 63RE Ch. 2 - Prob. 64RE Ch. 2 - Prob. 65RE Ch. 2 - Prob. 66RE Ch. 2 - Prob. 1CT Ch. 2 - Prob. 2CT Ch. 2 - Prob. 3CT Ch. 2 - Prob. 4CT Ch. 2 - Prob. 5CT Ch. 2 - Prob. 6CT Ch. 2 - Prob. 7CT Ch. 2 - Prob. 8CT Ch. 2 - Prob. 9CT Ch. 2 - Prob. 10CT Ch. 2 - Prob. 11CT Ch. 2 - Prob. 12CT Ch. 2 - Prob. 13CT Ch. 2 - Prob. 14CT Ch. 2 - Prob. 15CT Ch. 2 - Prob. 16CT Ch. 2 - Prob. 17CT Ch. 2 - Prob. 18CT Ch. 2 - Prob. 1PS Ch. 2 - Prob. 2PS Ch. 2 - Prob. 3PS Ch. 2 - Prob. 4PS Ch. 2 - Prob. 5PS Ch. 2 - Prob. 6PS Ch. 2 - Prob. 7PS Ch. 2 - Prob. 8PS Ch. 2 - Prob. 9PS Ch. 2 - Prob. 10PS Ch. 2 - Prob. 11PS Ch. 2 - Prob. 12PS Ch. 2 - Prob. 13PS

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