College Algebra
Graphing Transformations
a) Given the function f (x) = x^2 complete the following table. Must show all work for full credit.
f (x)
Show Work:
When x = 0, f (x) = f (0) = (0)^2 = 0.
When x = 1, f (x) = f (1) = (1)^2 = 1.
When x = 4, f (x) = f (4) = (4)^2 = 16.
When x = 9, f (x) = f (9) = (9)^2 = 81.
When x = 16, f (x) = f (16) = (16)^2 = 256.
b) Using the table from part a, graph the function f (x) = x^2 . For a tutorial on creating graphs in Excel and inserting graphs of functions please see the Assignment List.
c) Given the function f (x) = (x +1)^2 complete the following table. Must show all work for full credit.
f (x)
Show Work or Explain in Words:
When x = -1, f (x) = f (-1) = (-1 + 1)^2 = (0)^2 = 0.
When x = 0, f (x) = f (0) = (0 + 1)^2 = (1)^2 = 1.
When x = 3, f (x) = f (3) = (3 + 1)^2 = (4)^2 = 16.
When x = 8, f (x) = f (8) = (8 + 1)^2 = (9)^2 = 81.
When x = 15, f (x) = f (15) = (15 + 1)^2 = (16)^2 = 256.
d) Using the table from part c, graph the function f (x) = (x +1)^2 . For a tutorial on creating graphs in Excel and inserting graphs of functions please see the Assignment List.
Answer:
e) Given the graph of y=f (x) describe in words the transformation of y=f (x+1).
Answer:
The function f (x+1) is the transformation of f (x) where f (x) is moved one unit to the left.
2) Find the domain of the function and express the answer in interval notation. Explain in words or show the calculations for full credit.
a) f (x) = 3x - 1
Answer: The domain of the function f (x) = 3x -- 1 is all real numbers.
Show Work or Explain in Words:
The domain of the function is defined by the value of x where x is defined within the function. Because there is no x that makes the function undefined, the domain is all real numbers.
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
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