1. No category

Math Analysis Honors – Worksheet 4
Domain of a Function
Your attitude, not your aptitude, will determine your altitude. – Zig Ziglar
For #1-11, find the domain of each function.
1
f ( x ) = −5x + 4
2
f ( x) = x2 + 2
3
7
x
x +1
x
f ( x) = 2
x − 16
2x
f ( x) = 2
x −4
x−2
F ( x) = 3
x +x
h ( x ) = 3x − 12
8
G ( x) = 1 − x
9
f ( x) =
4
x−9
f ( x) =
2
x −1
4
5
6
10
f ( x) =
2
11
q ( x ) = −x − 2
12
If a rock falls from a height of 20 meters on Earth, the height H (in meters) after x seconds is approximately
H ( x ) = 20 − 4.9x 2
(a) What is the height of the rock when x = 1 second? x = 1.2 seconds? x = 1.4 seconds?
(b) When is the height of the rock 12 meters?
(c) When does the rock strike the ground?
Tiffany, a commissioned salesperson, earns $100 base pay plus $10 per item sold. Express her gross salary G as a
function of the number x items sold.
f ( x + h) − f ( x)
For f ( x ) = x 2 + 6x + 8 , evaluate
h
Find the equation of the line that passes through ( 3, −2 ) and is perpendicular to 2x + 5y = 10 .
13
14
15
Answers:
1) ( −∞, ∞ )
6)
( −∞, −3) ∪ ( −3, 0 ) ∪ ( 0, ∞ )
11) ( −∞, −2 )
2) ( −∞, ∞ )
3) ( −∞, ∞ )
4) x ≠ ±4
7) x ≥ 4
8) ( −∞,1)
9) ( 9, ∞ )
12) a) 15.1;
12.944; 10.396
b) 1.277 sec
c) 2.020 sec
13)
G ( x ) = 100 + 10x
14) 2x + h + 6
5)
( −∞, −2 ) ∪ ( −2, 2 ) ∪ ( 2, ∞ )
10) x ≥ 1
15) y − ( −2 ) =
5
( x − 3)
2