0Functions of one variable
(DEMO)
Reference book: Sydsaeter and Hammond
Play with Graphs- Arihant
Content plan for Day 1:
Graphs of Functions: Special focus on trigonometric functions. All basic functions like exponential, logarithmic and power functions will be covered.
Linear and quadratic functions: Domain, Range, Notations, optimisation problems.
Functions:
Definition: A real valued function is a function that assigns a unique real number to a real variable x in the domain D. The set of values f(x) taken by x is called the range of f.
Quadratic Functions: A function from R-R(n) taking the form ax(n) + bx(n-1)+ ........ +z , where a,b,.....z belong to R and a is not equal to 0.
Example: x^2+x+1
Linear function: A quadratic function with n=1.
Example: x+1
Domain and Range:
Domain is the input set
Range is the output set
Let us define f: R-R given by f(x)=x
then, The domain is R and the Range is also R.
This function is also known as identity function.
Optimisation:
f(x) = x^2
We optimise using derivatives.
f'(x) = 2x+2=0
f'' (x)= 2
We thus have a minimum as f'' >0
so, x=0
f(-1) = 2 which is the minimum value the function can take.
