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)...
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…
