3.3 FUNCTION NOTATION (PART 2)
g(x) = 2/5x – 1
f(x) = –2x + 4
Work
Problem
t is
Wha 3)?
–
h(
h(–3) = 7 – (–3)
=7+3
= 10
x
t is
Wha en
wh 4?
=
f(x )
t is
Wha 0)?
g(1
x
t is
Wha en
wh 1?
=
g(x)
h(x) = 7 – x
Answer
(in function notation!)
h(–3) = 10
1 =
+1
2 =
*5
10 =
/2
5 =
/5x – 1
+1
2/ x
5
*5
2x
/2
x
f(0) = 4
w(–2) = 1
What is w(3)?
g(10) = 3
So when x is 3, what is y? Find 3 on
the x-axis and follow down to the
graph...then see where that point falls
on y-axis.
w(3) = –3
2
What is x when w(x) = 2?
g(5) = 1
w(5) = 2
So when y is 2, what is x? Find 2 on
the y-axis and follow over to the
graph...then see where that point falls
on x-axis.
Use the graph of k(x) to answer the following
questions. Express all answers in complete function
k(x)
notation!
What is k(–6)?
Use the graph of p(x) to answer the following
questions. Express all answers in complete function
notation!
p(x)
What is x when
p(x) = 5?
So when x is -6, what is y? Find -6 on
the x-axis and follow up to the
graph...then see where that point falls
on y-axis.
p(–6) = 5
k(–6) = 4
What is x when
k(x) = 7?
So when y is 7, what is x? Find 7 on
the y-axis and follow over to the
graph...then see where that point falls
on x-axis.
What is w(–2)?
So when x is -2, what is y? Find -2 on
the x-axis and follow up to the
graph...then see where that point falls
on y-axis.
4 = –2x + 4
–4
–4
0 = –2x
/–2
/–2
0 = x
g(10) = 2/5(10) – 1
=4–1
=3
Use the graph of w(x) to answer the following
questions. Express all answers in complete function
w(x)
notation!
What is p(3)?
p(3) = –2
k(6) = 7
What is x when
p(x) = –6?
p(5) = –6
What is k(3)?
So when x is 3, what is y? Find 3 on the x-axis and follow up to the
graph...then see where that point falls on y-axis.
k(3) = 2
What is p(–3)?
p(–3) = 1
3.3 FUNCTION NOTATION (PART 2)
Interpreting Function Notation
Interpreting Function Notation
Let f(x) be the outside temperature ( F) x hours after
6:00 am. Explain the meaning of each statement.
Let h(x) be the percent of U.S. households with internet
use x years after 1980. Explain the meaning of each
statement.
a. h(23) = 55 In 2003, 55% of US households
had internet.
o
a. f(0) = 58 At 6:00 am, it was 58oF outside.
f(x) equals the temperature, so if it equals 58, then the
temperature was 58oF.
X is hours after 6:00 am.
So if x is 0, the time is 6:00 am.
b. f(6) = 20
At noon, it was 20oF outside.
f(x) equals the temperature, so if it equals 20, then the
temperature was 20oF.
X is hours after 6:00 am.
So 6 hours after 6:00 am is 12:00 pm (noon).
c. f(3) < f(9) At 9:00 am, the temperature was
lower than it was at 3:00pm.
is
X is hours
less
after 6:00 am. than
So 3 hours
after 6:00 am
is 9:00 am.
X is hours
after 6:00 am.
So 9 hours
after 3:00 pm.
Interpreting Function Notation
Let c(x) be the number of customers in a restaurant
x hours after 8:00 am. Explain the meaning of each
statement.
At 8:00 am, there were no people
a. c(0) = 0
in the restaurant.
f(x) equals the number of people in the restaurant, so if it
equals 0, then there were no people in the restaurant.
X is hours after 8:00 am.
So if x is 0, the time is 8:00 am.There were equal numbers of
b. c(3) = c(8)
is
equal
to
people in the restaurant at 11:00
am and 4:00 pm.
X is hours after 8:00 am.
So 8 hours after 8:00 am is 4:00 pm.
X is hours after 8:00 am.
So 3 hours after 8:00 am is 11:00 am.
c. c(6) < c(4) There were less people in the
restaurant at 2:00 pm than there
were at noon.
is
X is hours
less
after 8:00 am. than
So 6 hours
after 8:00 am
is 2:00 pm.
X is hours after 8:00 am.
So 4 hours after 12:00 pm (noon).
f(x) equals the percent of US households who have
internet. So if it equals 55, then 55% of US households
X is years after 1980. had internet.
23 years after 1980 is the year 2003.
b. h(27) ≥ 61
In 2007, at least 61% of US
households had internet.
Greater than
f(x) is percent of US households who have
or equal to,
aka: "at least" internet. So if it says 61, then 61% of US
households had internet.
X is years after 1980.
27 years after 1980 is the year 2007.
c. f(10) > f(5)
X is years after
1980. 10 years
after 1980 is
the year 1990.
is
greater
than
In 1990 there were more US
households with internet than
there were in 1985.
X is years after
1980. 5 years
after 1980 is
the year 1985.