Function Notation Worksheet
1. Evaluate the following expressions given the functions below:
a)
b)
c)
d)
e)
f)
g)
h) Find x if g(x) = 16
i) Find x if h(x) = -2
j) Find x if f(x) = 23
k) Find x if j(x) = -31
2. Translate the following statements into coordinate points:
a)
b)
c)
3. Given this graph of the function f(x):
f(x) 5
Find:
a)
b)
c)
d)
e) x if f(x) = -1
f) x if f(x) = 4
-5
y
5
x
-5
4. Which statement is true?
a) All functions are relations, but not all relations are functions.
b) All relations are functions, but not all functions are relations.
APPLICATION
5. Ivory the botanist treated a 2 cm plant with a special growth fertilizer. With this fertilizer, the
plant grew at a rate modelled by the function
, where
represents the height of
the plant in cm after days.
a) Determine the value of H(3).
b) Write in words the meaning of H(3).
c) Evaluate H(0), H(6) and H(21).
d) It takes 27 days for the plant to mature (reach max height). State the domain
and range of the function H(t).
6. Swine flu is attacking Porkopolis. The function below determines how many people have swine
flu, where t = time in days and S = the number of people in thousands.
a) Find S(4).
b) What does S(4) mean?
c) Find t when S(t) = 23.
d) What does S(t) = 23 mean?
7. As part of an experiment, a 50 kg steel ball is dropped from a Canadian Air Force jet. The height
of the steel ball above the ground can be described by part of the graph of the function
h(t) = 2575 - 4.9t2, where h(t) is the height in metres, of the steel ball after t seconds.
a) Determine the value of h(30)
b) Why does h(30) not represent the height of the ball after 30 seconds?
c) At what height is the ball dropped from the jet?
d) How long (to the nearest second) will it take the ball to make contact with the ground?
e) Suggest an appropriate domain and range for the function h(t).
8. a) Does the graph represent a function?
b) What is the value of
c) Find x if: i)
,
,
and
.
and ii)
9. Given f(x):
a) Find f(-2), f(0) and f(2)
b) Find x if f(x) = 1
Answers:
1. a) -29 b) 16 c) -6 d) 23 e) 2x + 13 f) x2 + 2x + 8 g) -6x – 26 h) -5 i) -6 j) ±4 k) -20
2. a) (-1,1) b) (2,7) c) (3,9)
3. a) 2 b) 0 c) -2 d) 0 e) 0.5 and 5 f) -2 4. a
5. a) 7cm b) height after 3 days c) 2,12,37 d)
;
6. a) 32 000 b) people with the flu after 4 days c) 3 d) 3days for 23 000 to have the flu
7. a) -1835 m b) Negative height not possible - ball has already hit the ground. c) 2575 m
d) 23 sec e) )
;
8. a) yes b) 5, 0.5, 4, 6 c) i. 2 ii.
9. a) 0, -2, 0 b) ±2.5