A museum charges $5 per person for a guided tour with a group of 1 to 9 people or a fixed $50 fee for a group of 10 or more people. Write a
function relating the number of people,
to the cost,
Two different formulas will be needed. For
n -values under 10,
For values of
that are 10 or greater,
Working with a piecewise function
A cell phone company uses the function below to determine the cost,
in dollars for
gigabytes of data transfer.
Find the cost of using 1.5 gigabytes of data and the cost of using 4 gigabytes of data.
To find the cost of using 1.5 gigabytes of data,
we first look to see which part of the domain our input falls in. Because 1.5 is less than 2, we use the first formula.
To find the cost of using 4 gigabytes of data,
we see that our input of 4 is greater than 2, so we use the second formula.
Given a piecewise function, sketch a graph.
Indicate on the
x -axis the boundaries defined by the intervals on each piece of the domain.
For each piece of the domain, graph on that interval using the corresponding equation pertaining to that piece. Do not graph two functions over one interval because it would violate the criteria of a function.
Graphing a piecewise function
Sketch a graph of the function.
Each of the component functions is from our library of toolkit functions, so we know their shapes. We can imagine graphing each function and then limiting the graph to the indicated domain. At the endpoints of the domain, we draw open circles to indicate where the endpoint is not included because of a less-than or greater-than inequality; we draw a closed circle where the endpoint is included because of a less-than-or-equal-to or greater-than-or-equal-to inequality.
[link] shows the three components of the piecewise function graphed on separate coordinate systems.
(a)
(b)
(c)
Now that we have sketched each piece individually, we combine them in the same coordinate plane. See
[link] .
Graph the following piecewise function.
Can more than one formula from a piecewise function be applied to a value in the domain?
No. Each value corresponds to one equation in a piecewise formula.
Access these online resources for additional instruction and practice with domain and range.
The domain of a function includes all real input values that would not cause us to attempt an undefined mathematical operation, such as dividing by zero or taking the square root of a negative number.
The domain of a function can be determined by listing the input values of a set of ordered pairs. See
[link] .
The domain of a function can also be determined by identifying the input values of a function written as an equation. See
[link] ,
[link] , and
[link] .
Interval values represented on a number line can be described using inequality notation, set-builder notation, and interval notation. See
[link] .
For many functions, the domain and range can be determined from a graph. See
[link] and
[link] .
An understanding of toolkit functions can be used to find the domain and range of related functions. See
[link] ,
[link] , and
[link] .
A piecewise function is described by more than one formula. See
[link] and
[link] .
A piecewise function can be graphed using each algebraic formula on its assigned subdomain. See
[link] .
Three charges q_{1}=+3\mu C, q_{2}=+6\mu C and q_{3}=+8\mu C are located at (2,0)m (0,0)m and (0,3) coordinates respectively. Find the magnitude and direction acted upon q_{2} by the two other charges.Draw the correct graphical illustration of the problem above showing the direction of all forces.
To solve this problem, we need to first find the net force acting on charge q_{2}. The magnitude of the force exerted by q_{1} on q_{2} is given by F=\frac{kq_{1}q_{2}}{r^{2}} where k is the Coulomb constant, q_{1} and q_{2} are the charges of the particles, and r is the distance between them.
Muhammed
What is the direction and net electric force on q_{1}= 5µC located at (0,4)r due to charges q_{2}=7mu located at (0,0)m and q_{3}=3\mu C located at (4,0)m?
Capacitor is a separation of opposite charges using an insulator of very small dimension between them. Capacitor is used for allowing an AC (alternating current) to pass while a DC (direct current) is blocked.
Gautam
A motor travelling at 72km/m on sighting a stop sign applying the breaks such that under constant deaccelerate in the meters of 50 metres what is the magnitude of the accelerate
velocity can be 72 km/h in question. 72 km/h=20 m/s, v^2=2.a.x , 20^2=2.a.50, a=4 m/s^2.
Mehmet
A boat travels due east at a speed of 40meter per seconds across a river flowing due south at 30meter per seconds. what is the resultant speed of the boat
which has a higher temperature, 1cup of boiling water or 1teapot of boiling water which can transfer more heat 1cup of boiling water or 1 teapot of boiling water explain your . answer
I believe temperature being an intensive property does not change for any amount of boiling water whereas heat being an extensive property changes with amount/size of the system.
Someone
Scratch that
Someone
temperature for any amount of water to boil at ntp is 100⁰C (it is a state function and and intensive property) and it depends both will give same amount of heat because the surface available for heat transfer is greater in case of the kettle as well as the heat stored in it but if you talk.....
Someone
about the amount of heat stored in the system then in that case since the mass of water in the kettle is greater so more energy is required to raise the temperature b/c more molecules of water are present in the kettle
pratica A on solution of hydro chloric acid,B is a solution containing 0.5000 mole ofsodium chlorid per dm³,put A in the burret and titrate 20.00 or 25.00cm³ portion of B using melting orange as the indicator. record the deside of your burret tabulate the burret reading and calculate the average volume of acid used?
No. According to Isac Newtons law. this two bodies maybe you and the wall beside you.
Attracting depends on the mass och each body and distance between them.
Dlovan
Are you really asking if two bodies have to be charged to be influenced by Coulombs Law?
Robert
like charges repel while unlike charges atttact
Raymond
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