IB Elite Tutor is providing the highest quality IB Maths Tutors. Learn IB Maths with us and get an assured 7. Get IB Maths AA HL Tutors, IB Maths AI HL Tutors, IB Maths AA SL Tutors, IB Maths AI HL Tutors, etc.
Sharpen your knowledge of Functions with IB Elite Tutors.
Domain and Range of a Function
IB Online Maths Tutors
Suppose I say that f is a real function.This means that for real input, the output should be real. For example is real, then can only take non negative values because only then the
F(x)=√x if f
x
If no domain is mentioned explicitly, the domain will be assumed to be such that f produces real output x∈(2,3) y=1∕x then domain will be any real number excluding zero Domain D=R {0}
output will be real. set of all real values of R is called domain
y=f(x)example,=x²;1<x>
⇒ ⇒ydomainy=f(x)=√xD:x≥0=f(x)=√x2∠x≤3 or
if
In some cases x is defined exlicitly. for here domain is defined explicitly as (1,2)
“Domain is the set of all possible inputs for which the output is real ”
if y=logx then domain will be any positive integer because logs are only defined for positive real numbers D≥1 Range- It is simply the set of possible outputs for a defined domain. Range depends upon domain domain1)Examples:y=x²x=ℝ Range y≥0 domain2)y=√x x≥0 range y≥0 3)y=√x 2∠x≤3 domain x=(2,3) range y=(√2,√3) To have a graphical picture in mind, consider this image
When plotted on a graph,the independent variable (x) is plotted on the horizontal axis while the dependent variable (y) is plotted on vertical axis
Suppsose y depends on x as shown in above figure. You can easily tell the domain and range of the function just by
looking at the above figure.
so Range R=c≤x≤d or
IN my next article I will discuss various types of functions
ToR=[c,d]summerze, for domain look along xaxis , for range look along y-axis
Domain D=a≤x≤b or lookD=[a,b]along the y axis and we see that the graph only varies only between certain values of y