SECTION 3.6 Function Notation and Linear Functions 195
35.Refer to Exercise 31.Find the value of xfor each value of .See Example 5(c).
(a) (b) (c)
36.Refer to Exercise 32.Find the value of xfor each value of. See Example 5(c).
(a) (b) (c)
An equation that defines y as a function f of x is given. (a)Solve for y in terms of x,and re-
place y with the function notation. (b)Find. See Example 6.
43.Concept Check Fill in each blank with the correct response.
The equation has a straight as its graph. One point that lies on the
graph is. If we solve the equation for yand use function notation, we obtain
. For this function, , meaning that the point ,
lies on the graph of the function.
44.Concept Check Which of the following defines yas a linear function of x?
A. B. C. D.
Graph each linear function. Give the domain and range. See Example 7.
48. 49. 50.
51. 52. 53. 54.
55.Concept Check What is the name that is usually given to the graph in Exercise 53?
56.Can the graph of a linear function have an undefined slope? Explain.
g 1 x 2 =- 4 ƒ 1 x 2 = 5 ƒ 1 x 2 = 0 ƒ 1 x 2 =-2.5
F 1 x 2 =- G 1 x 2 = 2 x H 1 x 2 =- 3 x
1
4
x+ 1
h 1 x 2 =
1
2
ƒ 1 x 2 =- 2 x+ 5 g 1 x 2 = 4 x- 1 x+ 2
y= y=x^2 y= 2 x
1
x
y=
1
4
x-
5
4
ƒ 1 x 2 = ƒ 132 = 1 2
1 3, 2
2 x+y= 4
y- 3 x^2 = 2 4 x- 3 y= 8 - 2 x+ 5 y= 9
x+ 3 y= 12 x- 4 y= 8 y+ 2 x^2 = 3
ƒ 1 x 2 ƒ 132
ƒ 1 x 2 = 4 ƒ 1 x 2 =- 2 ƒ 1 x 2 = 0
ƒ 1 x 2
ƒ 1 x 2 = 3 ƒ 1 x 2 =- 1 ƒ 1 x 2 =- 3
ƒ 1 x 2
Solve each problem.
57.A package weighing xpounds costs dollars to
mail to a given location, where
.
(a)Evaluate.
(b)Describe what 3 and the value mean in part (a),
using the terminology independent variableand
dependent variable.
(c) How much would it cost to mail a 5-lb package?
Interpret this question and its answer, using
function notation.
ƒ 132
ƒ 132
ƒ 1 x 2 =3.75x
ƒ 1 x 2
58.A taxicab driver charges $2.50 per mile.
(a)Fill in the table with the cor-
rect response for the price
he charges for a trip of
xmiles.
(b)The linear function that
gives a rule for the amount
charged is.
(c)Graph this function for the domain 5 0, 1, 2, 3 6.
ƒ 1 x 2 =
ƒ 1 x 2
x
0
1
2
3
ƒ 1 x 2