Polynomial functions, assignment help

Please complete the following questions. It is important that you show all work you did to solve the problems when you submit your work. This includes any calculations, diagrams, or graphs that helped you solve it. thank you .

Writing in Math Use the information aboutmedication on page 382 to explain how the roots of an equation can beused in pharmacology. Include an explanation of what the roots of thisequation represent and an explanation of what the roots of this equationreveal about how often a patient should take this medication. Page 382 is in the attachments. Writing in Math Refer to the informationon page 411 to explain how inverse functions can be used in measurementconversions. Point out why it might be helpful to know the customaryunits if you are given metric units. Demonstrate how to convert thespeed of light c = 3.0 × 108 meters per second to miles per hour. Page 411 is in the attachments. Main Ideas
• Find the inverse of a
function or relation.
• Determine whether
two functions or
relations are inverses
New Vocabulary
inverse relation
inverse function
identity function
one-to-one
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
f(x)
1 heur 1 mile
or f(x) = x
3600 seconds
To convert x meters per second to an approximate equivalent in miles
per hour, you can evaluate the following.
1 mile
8(x) = 4 meters. 3600 seconds
1 second 1 hour 1600 meters
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.
9
or g(x) = Ž
Page
141
Main Ideas
• Find the inverse of a
function or relation.
• Determine whether
two functions or
relations are inverses
New Vocabulary
inverse relation
inverse function
identity function
one-to-one
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
f(x)
1 heur 1 mile
or f(x) = x
3600 seconds
To convert x meters per second to an approximate equivalent in miles
per hour, you can evaluate the following.
1 mile
8(x) = 4 meters. 3600 seconds
1 second 1 hour 1600 meters
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.
9
or g(x) = Ž
Page
141
Main Ideas
• Find the inverse of a
function or relation.
• Determine whether
two functions or
relations are inverses
New Vocabulary
inverse relation
inverse function
identity function
one-to-one
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
f(x)
1 heur 1 mile
or f(x) = x
3600 seconds
To convert x meters per second to an approximate equivalent in miles
per hour, you can evaluate the following.
1 mile
8(x) = 4 meters. 3600 seconds
1 second 1 hour 1600 meters
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.
9
or g(x) = Ž
Page
141
Determine the
number and type
of roots for a
polynomial equation.
Find the zeros of a
polynomial function.
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) = 0.5+4 + 3.5+3 – 100+2 + 350t 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.
Page
Types of Roots You have already learned that a zero of a function f(x) is
any value o such that f(c) = 0. When the function is graphed, the real zeros
of the function are the x-intercepts of the graph.
387
KEY CONCEPT
Zeros, Factors, and Roots
Let f(x) = a, x” + … +0,x + a, be a polynomial function. Then the following
statements are equivalent.
• cis a zero of the polynomial function f(x).
• x- cis a factor of the polynomial f(x).
·cis a root or solution of the polynomial equation f(x)
In addition, if c is a real number, then (c, 0) is an intercept of the graph of f(x).
= 0.