Math 1010-001
Worksheet #3
Due 06/30/06
Name: ___________________________
In problems #1-4, match the functions with their graphs. Refer to your handout regarding
transformations of graphs of functions, or see p.198-200 of your text.
A
B
C
D
1.) f (x) = x 2 ______
!
!
!
!
2.) f (x) = (x "1) 2 ______
3.) f (x) = x 2 "1 ______
4.) f (x) = (x + 1) 2 ______
The next few problems are exercises in identifying the domain of a function. For our
purposes, the inputs and outputs of a function are real numbers. The domain is the set of
real numbers at which the function can be evaluated, and the range is the set of all possible
outputs. To determine the domain ask yourself at which points the function can NOT be
evaluated. Usually this is because of an undefined operation, which practically speaking
means dividing by zero, or extracting the square root of a negative number.
5.) Let the function f be defined by f (x) =
6x + 6
.
4x + 7
Then the domain of f contains all real numbers x except x = ______.
!
6.) Let the function f be defined by f (x) =
6x + 5 .
Then x is in the domain of f provided x " ______.
!
! by f (x) =
7.) Let the function f be defined
"9x + 3 .
Then x is in the domain of f provided x " ______.
!
!
In problems #8-10, let the function f be defined by f (x) =
following statements are true (T) or false (F).
8.) f (x) is never negative. ______
1
1" x 2
!
9.) 1 is in the domain of f. ______
10.) All positive real numbers are in the domain of f. ______
. Indicate whether the