MTH133
Unit 4– Individual Project – D

1. Graphing Transformations
a) Given the function f(x) = x2 complete the following table. Must show all work for full credit.
Answer:
x f(x)
-2 4
-1 1
0 0
1 1
2 4

Show your work here:
For x = -2, f(x) = (-2)2 = 4
For x = -1, f(x) = (-1)2 = 1
For x = 0, f(x) = (0)2 = 0
For x = 1, f(x) = (1)2 = 1
For x = 2, f(x) = (2)2 = 4

b) Using the table from part a, graph the function f(x) = x2. For a tutorial on creating graphs in Excel and inserting graphs of functions please see the Assignment List.
Answer:

c) Given the function f(x) = x2 - 4 complete the following table. Must show all work for full credit.
Answer:
x f(x)
-2 0
-1 -3
0 -4
1 -3
2 0

Show Work:
For x = -2, f(x) = (-2)2 – 4 = 4 – 4 = 0
For x = -1, f(x) = (-1)2 – 4 = 1 – 4 = 0-3
For x = 0, f(x) = (0)2 – 4 = 0 – 4 = -4
For x = 1, f(x) = (1)2 – 4 = 1 – 4 = -3
For x = 2, f(x) = (2)2 – 4 = 4 – 4 = 0

d) Using the table from part c, graph the function f(x) = x2 - 4. 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)-4.
Answer:
The graph of y=f(x)-4 is a 4 unit shift of the graph y = f(x) towards down.

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) = 10x + 1
Answer: domain is (-∞, ∞)
Show Work or Explain in Words:
The function f(x) satisfies for all the real numbers. That is if we substitute any real number in place of x, we can get another real number. So the domain of the function is (-∞, ∞).
b) g(x) = 6x2 – 9x
Answer: domain is (-∞, ∞)
Show Work or Explain in Words:
The function f(x) satisfies for all the real numbers. That is if we substitute any real number in place of x, we can get another real number. So the domain of the function is (-∞, ∞).
c) f(x) = 13/(x + 9)
Answer: domain is (-∞, -9) U (-9, ∞)
Show Work or Explain in Words:
X + 9 = 0
X = 0 -9
X = -9
The function is not defined for x = -9. So the domain is (-∞, -9) U (-9, ∞).
d) g(x) =
Answer: [2, ∞)
Show Work or Explain in Words:
7x – 14 ≥ 0
7x ≥ 14
X ≥ 14/7
X ≥ 2
e) 2x2/(x + 11)
Answer: domain is (-∞, -11) U (-11, ∞)
Show Work or Explain in Words: x + 11 = 0 x = -11
The function is undefined for x = -11, so the domain is (-∞, -11) U (-11, ∞).

3. Given the rational function f(x) = (8x – 3)/(4x + 12) explain in detail how to find the equations of the horizontal and vertical asymptotes. Be sure to conclude your explanation by giving the equations of the lines for the horizontal and vertical asymptotes.
Answer:
The highest power of the numerator, m =1
The highest power of the denominator, n =1
So, since m =n, the horizontal asymptote is y = 1.
The vertical asymptote is obtained by setting the denominator 0 and finding the value of x.
4x + 12 = 0
4x = -12
X = -12/4
X = -3
The vertical asymptote is x = -3.