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,
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.
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] .
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] .
Questions & Answers
A golfer on a fairway is 70 m away from the green, which sits below the level of the fairway by 20 m. If the golfer hits the ball at an angle of 40° with an initial speed of 20 m/s, how close to the green does she come?
A mouse of mass 200 g falls 100 m down a vertical mine shaft and lands at the bottom with a speed of 8.0 m/s. During its fall, how much work is done on the mouse by air resistance
Chemistry is a branch of science that deals with the study of matter,it composition,it structure and the changes it undergoes
Adjei
please, I'm a physics student and I need help in physics
Adjanou
chemistry could also be understood like the sexual attraction/repulsion of the male and female elements. the reaction varies depending on the energy differences of each given gender. + masculine -female.
Pedro
A ball is thrown straight up.it passes a 2.0m high window 7.50 m off the ground on it path up and takes 1.30 s to go past the window.what was the ball initial velocity
2. A sled plus passenger with total mass 50 kg is pulled 20 m across the snow (0.20) at constant velocity by a force directed 25° above the horizontal. Calculate (a) the work of the applied force, (b) the work of friction, and (c) the total work.
you have been hired as an espert witness in a court case involving an automobile accident. the accident involved car A of mass 1500kg which crashed into stationary car B of mass 1100kg. the driver of car A applied his brakes 15 m before he skidded and crashed into car B. after the collision, car A s
can someone explain to me, an ignorant high school student, why the trend of the graph doesn't follow the fact that the higher frequency a sound wave is, the more power it is, hence, making me think the phons output would follow this general trend?
Nevermind i just realied that the graph is the phons output for a person with normal hearing and not just the phons output of the sound waves power, I should read the entire thing next time
Joseph
Follow up question, does anyone know where I can find a graph that accuretly depicts the actual relative "power" output of sound over its frequency instead of just humans hearing
Joseph
"Generation of electrical energy from sound energy | IEEE Conference Publication | IEEE Xplore" ***ieeexplore.ieee.org/document/7150687?reload=true
A string is 3.00 m long with a mass of 5.00 g. The string is held taut with a tension of 500.00 N applied to the string. A pulse is sent down the string. How long does it take the pulse to travel the 3.00 m of the string?
