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1. All work must be done on your notebook paper. Work may NOT be done on the
worksheet itself.
2. For each problem, you must begin by writing the original problem on your
paper.
3. All work must be in order, neat, and written in pencil.
4. You may use your textbook,
and you may get help in the math lab (SAG 202).
Function Notation:
f (x) means f is a function of x and is read “f of x”. x is the input
and f(x) is the output.
Examples of function notations and related meanings:
For a given function f,
f (2) gives the input for x as 2. You replace x with 2 and calculate the
output.
f (x) = 5 gives the output as 5. You replace f (x) with 5 and find x.
Function Exercises:
1. f (x) = 3x – 5
Find f (-3).
2. f (x) = 2x + 9
Find 
.
3. 
Find 
.
4. 
Find f (-5).
5. 
Find f (-2).
(Remember order of operations and calculate the exponential expression before
multiplying).
6. f (x) = 3x -5
Find x such that f (x) = 7.
7. f (x) = -2x + 11
Find x such that f (x) = 38.
Domain and Range:
The domain of a function is the set of valid inputs (x-values). The range of a
function is the set of outputs (y-values).
Given a graph of a function, the domain is the set of all x-values of points
on the graph (the horizontal span of the graph). The range is the set of all
y-values of points on the graph (the vertical span of the graph).
Determining the domain for a given function:
A number is NOT in the domain of a function if:
a) it results in division by 0
b) it results in taking the square root of a negative number
If a function represented by an equation does not contain
a fraction or a square root, the domain is the set of all real numbers, which
is the interval 
.
From the following graph, answer problems 8, 9, and 10.
8. Find f (-1).
9. Find x such that f (x) = 4.
10. Find the domain of the function.
From the following graph, answer problems 11 and 12.
11. Find f (0).
12. Find the range of the function.
13. Find the domain of 
.
14. Find the domain of 
.
15. Find the domain of 
.
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