Download FMa 10 Ch 5.2 HW key

Math 10
Unit 5
Relations and Functions
Name:_____Key_________
Assignment: 5.2
1. Which arrow diagrams represent functions?
2. Which sets of ordered pairs represent functions? Identify the domain and range of
each set of ordered pairs.
a) {(1, 3), (2, 6), (3, 9), (4, 12)}
Function; domain: {1, 2, 3, 4}; range: {3, 6, 9, 12}
b) {(1, 0), (0, 1), (–1, 0), (0, –1)}
Not a function; domain: {–1, 0, 1}; range: {–1, 0, 1}
c) {(2, 3), (4, 5), (6, 7), (8, 9)}
Function; domain: {2, 4, 6, 8}; range: {3, 5, 7, 9}
d) {(0, 1), (0, 2), (1, 2), (0, 3), (1, 3), (2, 3)}
Not a function; domain: {0, 1, 2}; range: {1, 2, 3}
3. Write in function notation.
a) C = 20n + 8
C(n) = 20 n + 8
c) t = 5 d
t(d) = 5 d
b) P = n – 3
P(n) = n – 3
d) y = – x
f(x) = – x
4. Write as an equation in two variables.
a) d(t) = 3t – 5
b) f (x) = –6x + 4
d = 3t – 5
y = –6x + 4
c) C(n) = 5 n
d) P(n) = 2n – 7
C=5n
P = 2n – 7
5. For each relation below:
■ Determine whether the relation is a function. Justify your answer.
■ Identify the domain and range of each relation.
a) {(1, 1), (2, 8), (3, 27), (4, 64)}
Function, it is one to one.
domain: {1, 2, 3, 4}; range: {1, 8, 27, 64}
b) {(3, 4), (3, 5), (3, 6), (3, 7)}
Not a function because 1 domain matches to 3 different ranges.
domain: {3}; range: {4, 5, 6, 7}
6. For each table of values below:
i) Explain why the relation is a function.
ii) Identify the independent variable and the dependent variable. Justify your
choices.
iii) Write the domain and range.
Function because each domain
matches a different range. (1 to 1)
Independent variable:
Number of cans of juice purchased.
Dependent variable:
Cost.
Domain: {1, 2, 3, 4, 5, 6 };
range: {2.39, 4.00, 6.39, 8.00, 10.39, 12.00 }
Function because each domain
matches a different range. (1 to 1)
Independent variable:
Altitude.
Dependent variable:
Temperature.
Domain: {610, 1220, 1830, 2440, 3050,
3660 };
range: {15.0, 11.1, 7.1, 3.1, –0.8, –4.8 }
7. For the function f (x) = – 5x + 11, determine:
a) f (1)
b) f (–3)
f (1) = – 5(1) + 11 = 6
f (–3) = – 5(–3) + 11 = 26
c) f (0)
d) f (1.2)
f (0) = – 5(0) + 11 = 11
f (1.2) = – 5(1.2) + 11 = 5
8. a) For the function f (n) = 2n – 7, determine n when:
i) f (n) = 11
ii) f (n) = – 6
11 = 2n – 7
– 6 = 2n – 7
b) For the function g(x) = – 5x + 1, determine x when:
i) g(x) = 41
ii) g(x) = – 16
41 = – 5x + 1
–16 = – 5x + 1
9. The function C(i) = 2.54 i converts a measurement of i inches to a measurement of
C centimetres.
a) Write the function as an equation in 2 variables.
C = 2.54 i
b) Determine the value of C(12).What does this number represent?
C(12) = 2.54 (12) = 30.48 ; this number represents "cm" if domain is
12 inches.
c) Determine the value of i when C(i) = 100. What does this number represent?
C(i) = 100 =2.54 i
,
i=
100
 39.37
2.54
This number represents "in" if range is 100 cm.
10. A car is traveling toward Meadow Lake Park, Saskatchewan. The equation
D = –80t + 300 represents the distance, D kilometres, to Meadow Lake after t
hours of driving.
a) Describe the function. Write this equation in function notation.
D(t) = –80t + 300
b) How far away from Meadow Lake Park was the car at the start of its journey?
How do you know?
At the start of the journey, t = 0, if substitute 0 for t.
D(0) = –80 (0) + 300 = 300 km
5
9
11. The function C(f ) = (f –32) converts a temperature, f degrees Fahrenheit, to C
degrees Celsius.
a) Determine:
i) C(50)
5
9
C(50) = (50 –32) = 10° C
ii) C(–13)
5
9
C(–13) = (–13 –32) = –25° C
b) Determine each value of f when:
i) C(f ) = 20
ii) C(f ) = –35
c) Write an equation in function notation to relate the temperatures in each fact.
i) Pure water freezes at 0°C or 32°F.
ii) Cookies are baked at 180°C or 356°F.