Q:

Provide a suitable domain and range to complete the definition of each function.a. Let f(x) = 2x + 3.b. Let f(x) = 2x.c. Let C(x) = 9x + 130, where C(x) is the number of calories in a sandwich containing x grams of fat.d. Let B(x) = 100(2)x, where B(x) is the number of bacteria at time x hours over the course of one day.

Accepted Solution

A:
Answer:Step-by-step explanation:We  have to find the domain and range of each function.a.[tex]f(x)=2x+3[/tex]It is a linear function because the degree of function is 1.Linear function is defined for all real values of x.Therefore, the domain of given function=RWhen we substitute real values in the given function then we get again real values.Therefore, range of f=Rb.[tex]f(x)=2x[/tex]It is a linear function .Domain=RRange=Rc.[tex]C(x)=9x+130[/tex]C(x)=Number of calories in a sandwich containing x grams of fat.x=Mass of fat Mass is always a natural number.Domain of C=NSubstitute x=1C(1)=9(1)+130=139C(2)=9(2)+130=18+130=148Range of C={139,148,157,...}d.[tex]B(x)=100(2)^x[/tex]B(x)=Number of bacteriax=Time in hoursNumber of bacteria is a natural number and time is always a whole number.Domain=WSubstitute x=0[tex]B(0)=100(2)^0=100[/tex][tex]B(1)=100(2)^1=200[/tex][tex]B(2)=100(2)^2=400[/tex]Range of B={100,200,200,800,...}