Essay: College Algebra Graphing Transformations

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SAMPLE EXCERPT:

[. . .] b) g (x)= (x+5)^2

Answer: The domain of the function g (x) = (x + 5)^2 is all real numbers.

Show Work or Explain in Words:

Like a), the domain of g (x) is defined for every value of x, therefore the domain of g (x) is all real numbers.

c) f (x)= 16x / x^2 +9

Answer: The domain of the function f (x)= 16x / x^2 + 9 is all real numbers.

Show Work or Explain in Words:

The domain of f (x) is defined for every value of x, therefore the domain of f (x) is all real numbers.

d) g (x)=13x^2 / 5x+9

Answer: The domain of g (x) is defined for every value of x, except where x = -1.8.

Show Work or Explain in Words:

The domain of g (x) is defined for every value of x, except where the denominator is 0. Because 5x + 9 = 0 where x = -1.8, it stands to reason that the domain of the function has a discontinuity at -1.8.

e) f (x)= 6 / x^5

Answer: The domain of f (x) is defined for every value of x.

Show Work or Explain in Words:

The domain of f (x) has a denominator that never amounts to 0, therefore every value of x is defined.

3. Finding equations of asymptotes of rational functions. Recall that asymptotes are lines therefore the Answer must be given as an equation of a line.

a) Find the equations of both the horizontal and vertical asymptotes of the rational function f (x) = 5x-1 / x^2 +9

Answer: There are no horizontal asymptotes. There are vertical asymptotes where y = -1 and y = 1.

Horizontal: None.

Vertical: The range falls where -1 < f (x) < 1.

Show Work or Explain in Words:

All values of x is defined in the function f (x), therefore the domain is all real numbers. The function, however, only works under a specific range, where the values of f (x) for x is no lesser than -1 and no greater than 1.

b) Find the equations of both the horizontal and vertical asymptotes of the rational function f (x) = 2x^2 + 8 / x-1

Answer: The horizontal asymptote is at x = 1.… [END OF PREVIEW]

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College Algebra Graphing Transformations.  (2011, September 15).  Retrieved May 25, 2019, from https://www.essaytown.com/subjects/paper/college-algebra-graphing-transformations/4066263

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"College Algebra Graphing Transformations."  15 September 2011.  Web.  25 May 2019. <https://www.essaytown.com/subjects/paper/college-algebra-graphing-transformations/4066263>.

Chicago Format

"College Algebra Graphing Transformations."  Essaytown.com.  September 15, 2011.  Accessed May 25, 2019.
https://www.essaytown.com/subjects/paper/college-algebra-graphing-transformations/4066263.