Some functions are defined by mathematical rules or procedures expressed in
equation form. If it is possible to express the function output with a
formula involving the input quantity, then we can define a function in algebraic form. For example, the equation
expresses a functional relationship between
and
We can rewrite it to decide if
is a function of
Given a function in equation form, write its algebraic formula.
Solve the equation to isolate the output variable on one side of the equal sign, with the other side as an expression that involves
only the input variable.
Use all the usual algebraic methods for solving equations, such as adding or subtracting the same quantity to or from both sides, or multiplying or dividing both sides of the equation by the same quantity.
Finding an equation of a function
Express the relationship
as a function
if possible.
To express the relationship in this form, we need to be able to write the relationship where
is a function of
which means writing it as
Does the equation
represent a function with
as input and
as output? If so, express the relationship as a function
First we subtract
from both sides.
We now try to solve for
in this equation.
We get two outputs corresponding to the same input, so this relationship cannot be represented as a single function
If we graph both functions on a graphing calculator, we will get the upper and lower semicircles.
Are there relationships expressed by an equation that do represent a function but that still cannot be represented by an algebraic formula?
Yes, this can happen. For example, given the equation
if we want to express
as a function of
there is no simple algebraic formula involving only
that equals
However, each
does determine a unique value for
and there are mathematical procedures by which
can be found to any desired accuracy. In this case, we say that the equation gives an implicit (implied) rule for
as a function of
even though the formula cannot be written explicitly.
Questions & Answers
Discuss the differences between taste and flavor, including how other sensory inputs contribute to our perception of flavor.
The lymphatic system plays several crucial roles in the human body, functioning as a key component of the immune system and contributing to the maintenance of fluid balance. Its main functions include:
1. Immune Response: The lymphatic system produces and transports lymphocytes, which are a type of
asegid
to transport fluids fats proteins and lymphocytes to the blood stream as lymph
Anatomy is the study of the structure of the body, while physiology is the study of the function of the body. Anatomy looks at the body's organs and systems, while physiology looks at how those organs and systems work together to keep the body functioning.
Enzymes are proteins that help speed up chemical reactions in our bodies. Enzymes are essential for digestion, liver function and much more. Too much or too little of a certain enzyme can cause health problems
Kamara
yes
Prince
how does the stomach protect itself from the damaging effects of HCl
the normal temperature is 37°c or 98.6 °Fahrenheit is important for maintaining the homeostasis in the body
the body regular this temperature through the process called thermoregulation which involves brain skin muscle and other organ working together to maintain stable internal temperature
