A function is a relation between a set A to set B that relates each element of set A to unique element of set B.
As an example consider a function defined for set of real numbers to set of real numbers as f(x)=2x+3.
f:R→Rf(x)=2⋅x+3
Here, the function is defined from real number to real number and variable in the function is x.
To determine
(b)
To define:
The domain and range of a function.
Expert Solution
Explanation of Solution
A functionf, which relates each element of set A to unique element of set B.
The set of each element of set A which is an input for function f is called the domain of function f.
The set of each element of set B which is an output of function f is called the range of a function f.
Also, the domain of a function f(x) is the range of its inverse function f−1(x) and vice-versa.
To determine
(c)
To define:
The graph of a function.
Expert Solution
Explanation of Solution
Assume a functionfis a relation between a set A to set B that relates each element of set A to unique element of set B.
The graphof a functionfis the set of allordered pairs (x,f(x)), such thatxis in thedomain of the functionf, wherexand f(x) arereal numbers.
These pairs are Cartesian coordinates of points in the Euclidean plane.
To determine
(d)
To define:
The dependent and independent variable.
Expert Solution
Explanation of Solution
A symbol that stands for an arbitrary input is called anindependent variable, while a symbol that stands for an arbitrary output is called adependent variable.
In a function f, the domain is the input for function which is independent variable as it is taken by choice.
The range is output in function f which depends upon the choice of input, so it is a dependent variable.
For example, consider a function y=2x+3x2. Here, the variable x is a dependent variable and the variable y is an independent variable.
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Homeruns A baseball analyst wishes to find a functionthat relates the distance, d, of a homerun and the speed, s,of the ball off the bat. Consider the data shown to theright.(a) Does the relation defined by the set of orders pairs(s, d) represent a function?(b) Draw a scatter diagram of the data, treating speed offbat as the independent variable.(c) Using a graphing utility, find the line of best fit thatmodels the relation between the speed off the bat andthe distance of the homerun?(d) Interpret the slope.(e) Express the relationship found in part (c), using functionnotation.(f) What is the domain of the function?(g) Predict the homerun distance if the speed of the ball offthe bat is 103 miles per hour.Mixed Practice
20. Hurricanes The following data represent the atmosphericpressure p (in millibars) and the wind speed w (in knots)measured during various tropical systems in the Atlantic Ocean.
Speed Off Bat (mph), s Homerun Distance (feet), d98 36999 381100 380100 397101 400102…
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