Polynomial Functions, assignment help

1. OPEN ENDED Give an example of an equation that is not quadratic but can be written in quadratic form. Then write it in quadratic form.
2. OPEN ENDED Write a set of ordered pairs for functions f and g, given that f ∘ g = {(4, 3), (-1, 9), (-2, 7)}.
3. Writing in Math Use the information about medication on page 382 to explain how the roots of an equation can be used in pharmacology. Include an explanation of what the roots of this equation represent and an explanation of what the roots of this equation reveal about how often a patient should take this medication.
4. Writing in Math Refer to the information on page 411 to explain how inverse functions can be used in measurement conversions. Point out why it might be helpful to know the customary units if you are given metric units. Demonstrate how to convert the speed of light c = 3.0 × 108 meters per second to miles per hour.

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Roots and Zeros
GET READY for the Lesson
When doctors prescribe medication, they give patients
instructions as to how much to take and how often it should be
taken. The amount of medication in your body varies with time.
Suppose the equation M(t) = 0.514 + 3.543 – 10012 + 350+ models
the number of milligrams of a certain medication in the bloodstream
t hours after it has been taken. The doctor can use the roots of
this equation to determine how often the patient should take the
medication to maintain a certain concentration in the body.
Types of Roots You have already learned that a zero of a function f(x) is
any value c such that f(c) = 0. When the function is graphed, the real zeros
of the function are the x-intercepts of the graph.
KEY CONCEPT
Zeros, Factors, and Roots
Let f(x) = 4, *” + … + ax + a, be a polynomial function. Then the following
statements are equivalent.
• c is a zero of the polynomial function f(x).
• x- cis a factor of the polynomial f(x).
c is a root or solution of the polynomial equation f(x) = 0.
In addition, if c is a real number, then (c, 0) is an intercept of the graph of f(x).
The graph of f(x) = x4 – 5×2 + 4 is shown at the
right. The zeros of the function are -2,-1, 1, and
2. The factors of the polynomial are x + 2, x + 1,
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AUG
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and mento
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GET READY for the Lesson
Most scientific formulas involve measurements given in SI
(International System) units. The SI units for speed are meters per
second. However, the United States uses customary measurements
such as miles per hour.
To convert x miles per hour to an approximate equivalent in meters
per second, you can evaluate the following.
x miles 1600 meters 1 hour
fx) =
1 hour 1 mile
To convert x meters per second to an approximate equivalent in miles
per hour, you can evaluate the following.
8(x) = 4 meters. 3600 seconds
1 mile
1 second 1 hour
or g(x) =
Notice that f(x) multiplies a number by 4 and divides it by 9. The
function g(x) does the inverse operation of f(x). It divides a number by
4 and multiplies it by 9. These functions are inverses.
3600 seconds or f(x) = *
1600 meters
Find Inverses Recall that a relation is a set of ordered pairs. The inverse
relation is the set of ordered pairs obtained by reversing the coordinates
of each ordered pair. The domain of a relation becomes the range of the
inverse, and the range of a relation becomes the domain of the inverse.
KEY CONCEPT
Inverse Relations
Words Two relations are inverse relations if and only if whenever one
relation contains the element (a, b), the other relation contains
the element (b, a).
Examples Q = {(1, 2), (3, 4), (5, 6)] S = {(2, 1), (4, 3), (6,5)]
Q and S are inverse relations.
EXAMPLE Find an Inverse Relation
GEOMETRY The ordered pairs of the relation {(2, 1), (5, 1), (2, -4)}
are the coordinates of the vertices of a right triangle. Find the
inverse of this relation and determine whether the resulting
ordered pairs are also the vertices of a right triangle.
To find the inverse of this relation, reverse the coordinates of the
ordered pairs.
(continuerl’ on the next page)
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