To evaluate
we substitute the value 4 for the input variable
in the given function.
Therefore, for an input of 4, we have an output of 24.
Given the function
evaluate
Solving functions
Given the function
solve for
If
either
or
(or both of them equal 0). We will set each factor equal to 0 and solve for
in each case.
This gives us two solutions. The output
when the input is either
or
We can also verify by graphing as in
[link] . The graph verifies that
and
Given the function
solve
Evaluating functions expressed in formulas
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
Therefore,
as a function of
is written as
Expressing the equation of a circle as a function
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
express
as a function of
Are there relationships expressed by an equation that do represent a function but which 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.
the transfer of energy by a force that causes an object to be displaced; the product of the component of the force in the direction of the displacement and the magnitude of the displacement
A wave is described by the function D(x,t)=(1.6cm) sin[(1.2cm^-1(x+6.8cm/st] what are:a.Amplitude b. wavelength c. wave number d. frequency e. period f. velocity of speed.
A body is projected upward at an angle 45° 18minutes with the horizontal with an initial speed of 40km per second. In hoe many seconds will the body reach the ground then how far from the point of projection will it strike. At what angle will the horizontal will strike
Suppose hydrogen and oxygen are diffusing through air. A small amount of each is released simultaneously. How much time passes before the hydrogen is 1.00 s ahead of the oxygen? Such differences in arrival times are used as an analytical tool in gas chromatography.
the science concerned with describing the interactions of energy, matter, space, and time; it is especially interested in what fundamental mechanisms underlie every phenomenon