Because the dots and circles overlap, the graph will cover all possible values of x, so the domain is all real numbers.
Study Guide and Review - Chapter 9
The range is all integers.
49. f (x) =
SOLUTION:
Make a table of values.
x
2x
f (x)
0
0
0
0.25
0.5
0
0.5
1
1
1
2
2
1.25
2.5
2
1.5
3
3
2
4
4
Because the dots and circles overlap, the graph will cover all possible values of x, so the domain is all real numbers.
The range is all integers.
50. f (x) = |x|
SOLUTION:
Since f (x) cannot be negative, the minimum point of the graph is where f (x) = 0.
Make a table of values. Be sure to include the domain values for which the function changes.
x
−2
−1
0
1
2
f (x)
2
1
0
1
2
The graph will cover all possible values of x, so the domain is all real numbers. The graph will go no lower than y = 8,
so the range is {y | y
0}.
51. f (x) = |2x − 2|
SOLUTION:
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Since f (x) cannot be negative, the minimum point of the graph is where f (x) = 0.