Individual Project
Use the graph of f (x) = x2 to match the function to its corresponding graph. In words describe the transformation that occurs (ex: The graph of f (x) is shifted 6 units to the left).
f (x) = x^
Choose from the following functions:
g (x) = (x -- 2)^2; h (x) = x^2 -- 2; i (x) = (x + 3)^2; j (x) = (x + 1)^2 + 3
a) Answer: i (x)
Function: (x+3)^
Description of transformation: The function is shifted to the left 3 units.
b) Answer: h (x)
Function: x^2-2
Description of transformation: The function is shifted down 2 units.
c) Answer: j (x)
Function: (x+1)^2 +
Description of transformation: The function is shifted to the left 1 unit and up 3 units.
d) Answer: g (x)
Function: (x -- 2)^
Description of transformation: The function is shifted to the right 2 units.
Find the domain of the function and express the answer in interval notation. Explain in words or show the calculations.
a) f (x) = 4x^2 -- 7x +
Answer: x is all real numbers
b) g (x) = 10 / (x+7)
Answer: x for all values except -7
Show Work or Explain in Words: The function g (x) becomes undefined when x+7 = 0. Consequently, x + 7 = 0 when x = -7. Therefore, the function is continuous for all values of x except x = -7. The domain then stands that x = all real numbers EXCEPT -7.
c) f (x) = sqrt (4x -- 16)
Answer: x is equal to or greater than 4
Show Work or Explain in Words: The function f (x) is never negative, the square root will always be positive. Therefore, the value of x has to be where 4x -- 16 is either equal to or greater than 0. Thus, the domain has to be where x is greater than or equal to 4.
d) g (x) = 2x / (x-3)
Answer: x for all values except 3
Show Work or Explain…
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