Posted: December 21st, 2022

Section 3.1: exercises 2, 18, 24, 64

Section 3.2: exercises 2, 14, 20, 28, 34, 46

Section 3.3: exercises 14, 18, 30, 44, 52, 58

Section 3.4: exercises 12*, 18*, 32*, 48, 58

Section 3.6: exercises 14, 28, 40, 52

SECTION 3.1 QUADRATIC FUNCTIONS AND MODELS

2. You are given an equation and the graph of a quadratic function.

a. Give the domain and range

b. Give the coordinates of the vertex

c. Give the equation of the axis

d. Find the y-intercept

e. Find the x-intercepts

(SEE PICTURE)

18. Graph each quadratic function. Give the (a) vertex, (b) axis, (c) domain, and (d)

range. Then determine (e) the interval of the domain for which the function is increasing

and (f) the interval for which the function is decreasing.

24.

64. According to data from the National Highway Traffic Safety Administration, the

accident rate as a function of the age of the driver in years x can be approximated by the

function

SECTION 3.2 SYNTHETIC DIVISION

2. Use synthetic division to perform the division

14.

20. Express f(x) in the form f(x)=(x-k)q(x)+r for the given value of k

28. For each polynomial function, use the remainder theorem and synthetic division to

find f(k)

34.

46. Use synthetic division to decide whether the given number k is a zero of the given

polynomial function. If it is not, give the value of f(k)

SECTION 3.3 ZEROS OF POLYNOMIAL FUNCTIONS

14. Use the factor theorem and synthetic division to decide whether the second

polynomial is a factor of the first

18. Factor f(x) into linear factors given that k is a zero of f(x)

30. For each polynomial function, one zero is given. Find all others.

44. For each polynomial function, find all zeros and their multiplicities

52. Find a polynomial function f(x) of degree 3 with real coefficients that satisfies the

given conditions.

58. Find a polynomial function f(x) of least degree having only real coefficients with

zeros as given.

SECTION 3.4 POLYNOMIAL FUNCTIONS: GRAPHS, APPLICATIONS, AND

MODELS

12*Sketch the graph of each polynomial function. Determine the intervals of the domain

for which function is (a) increasing or (b) decreasing

18*

32* Graph each polynomial function. Factor first if the expression is not in factored form.

48. Use the intermediate value theorem or polynomials to show that each polynomial

function has a real zero between the numbers given.

58. Show that the real zeros of each polynomial function satisfy the given conditions

SECTION 3.6 VARIATION

14. Solve each variation

If (m) varies jointly as z and p, and m=10 when z=2 and p=7.5, find m when z=6 and

p=9

28. The current in a simple electrical circuit varies inversely as the resistance. If the

current is 50amps when the resistance is 10ohms, find the current if the resistance is

5ohms.

40. The number of long-distance phone calls between two citites in a certain time period

varies directly as the populations of the cities and inversely as the distance between

them. If 10,000 calls are made between two citites 500 mi apart, having populations of

50,000 and 125,000, find the number of calls between two citites 800mi apart, having

populations of 20,000 and 80,000.

52. Suppose y is inversely proportional to x, and x is tripled. What happens to y?

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