Individual Project Use the Graph of F Essay

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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.

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a) f (x) = 4x^2 -- 7x +

Answer: x is all real numbers

Show Work or Explain in Words: The domain of a function is defined where all values of x is a real number. Because there is no instance where the function f (x), which is a quadratic function, becomes undefined, it stands that all values of x is continuous. Thus the domain of f (x) is where x encompasses the value of 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

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