Posted: January 24th, 2021
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
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.
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
SECTION 3.2 SYNTHETIC DIVISION
2. Use synthetic division to perform the division
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
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
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
12*Sketch the graph of each polynomial function. Determine the intervals of the domain
for which function is (a) increasing or (b) decreasing
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
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
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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