BB - Functions (Operations and Piecewise)
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This document introduces functions and function notation. It defines a function as a rule that takes an input and produces an output. It shows examples of functions written in function notation like f(x)=3x and evaluates functions for given inputs. It discusses operations that can be performed on functions like addition, subtraction, multiplication, and composition. It provides examples of evaluating these operations. It also gives real-life examples of functions modeling jeepney fares and investment growth. Finally, it introduces piecewise functions and gives an example of a piecewise function modeling guide fees.
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please sir i want to comments of every code what i do in eachline . in this w...
please sir i want to comments of every code what i do in eachline .
in this way i good understand this programme.
thanks sri..........
class String
{
public:
string str;
String(string s)
{
str=s;
}
void print(){
cout<<str;
}
String operator+(String obj)
{
string s1=str + obj.str;
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};
template <class myType>
myType add(myType a, myType b) {
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}
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{
int i1,i2;
float f1,f2;
string s1,s2;
cout<<"Enter Integer values:";
cin>>i1>>i2;
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please sir i want to comments of every code what i do in eachline .
in this way i good understand this programme.
thanks sri..........
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{
public:
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}
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{
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};
template <class myType>
myType add(myType a, myType b) {
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}
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{
int i1,i2;
float f1,f2;
string s1,s2;
cout<<"Enter Integer values:";
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cin>>f1>>f2;
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cin>>s1>>s2;
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Youtube: https://www.youtube.com/channel/UCGEKILGmI9zSn6nRfkrbblw?view_as=subscriber
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4. operators in c programming by digital wave
For Video Tutorial Click on Link:
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please sir i want to comments of every code what i do in eachline . in this w...
please sir i want to comments of every code what i do in eachline .
in this way i good understand this programme.
thanks sri..........
class String
{
public:
string str;
String(string s)
{
str=s;
}
void print(){
cout<<str;
}
String operator+(String obj)
{
string s1=str + obj.str;
return String(s1);
}
};
template <class myType>
myType add(myType a, myType b) {
myType res;
res = a+b;
return res;
}
int main()
{
int i1,i2;
float f1,f2;
string s1,s2;
cout<<"Enter Integer values:";
cin>>i1>>i2;
cout<<"Sum is :"<<add(i1,i2)<<endl;
cout<<"\nEnter float values:";
cin>>f1>>f2;
cout<<"Sum is :"<<add(f1,f2)<<endl;
cout<<"Enter two strings";
cin>>s1>>s2;
String str1(s1);
String str2(s2);
String str = add(s1,s2);
cout<<"sum is ";str.print();
cout<<endl;system("pause");
}
please sir i want to comments of every code what i do in eachline .
in this way i good understand this programme.
thanks sri..........
class String
{
public:
string str;
String(string s)
{
str=s;
}
void print(){
cout<<str;
}
String operator+(String obj)
{
string s1=str + obj.str;
return String(s1);
}
};
template <class myType>
myType add(myType a, myType b) {
myType res;
res = a+b;
return res;
}
int main()
{
int i1,i2;
float f1,f2;
string s1,s2;
cout<<"Enter Integer values:";
cin>>i1>>i2;
cout<<"Sum is :"<<add(i1,i2)<<endl;
cout<<"\nEnter float values:";
cin>>f1>>f2;
cout<<"Sum is :"<<add(f1,f2)<<endl;
cout<<"Enter two strings";
cin>>s1>>s2;
String str1(s1);
String str2(s2);
String str = add(s1,s2);
cout<<"sum is ";str.print();
cout<<endl;system("pause");
}
What's hot (19)
please sir i want to comments of every code what i do in eachline . in this w...
please sir i want to comments of every code what i do in eachline . in this w...
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BB - Functions (Operations and Piecewise)
- 2. The Function Rule • A function can be thought of as a rule which operates on an input and produces and output.
- 3. The Function Notation 𝑓 𝑥 = 3𝑥 • Read as “𝒇 as a function of 𝒙” or “𝒇 of 𝒙” or “the rule of 𝒇 is….” • meaning that the value of the output from the function depends upon the value of the input x. • The value of the output is often called the ‘value of the function’. Name of the function Input Output (value of the function)
- 4. The Function Notation Given the following functions, find the value of the output with each given input or argument: 1. Given: 𝑓 𝑥 = 3𝑥 + 1 i. 𝑓 2 ii. 𝑓 −1 iii. 𝑓(6) 2. Given: 𝑦 𝑥 = 3𝑥 + 2 i. 𝑦 𝑡 ii. 𝑦 2𝑡 iii. 𝑦(𝑧 + 2)
- 5. The Function Notation Given the following functions, find the value of the output with each given input or argument: 3. 𝑔 𝑥 = 3𝑥2 − 7 i. 𝑔(3𝑡) ii. 𝑔 𝑡 + 5
- 6. Operations on Functions •Similar to any real numbers, functions can also be added, subtracted, multiplied and divided. EQUATION OPERATION 𝒇 + 𝒈 𝒙 = 𝒇 𝒙 + 𝒈(𝒙) Addition 𝑓 − 𝑔 𝑥 = 𝑓 𝑥 − 𝑔(𝑥) Subtraction 𝑓 ∙ 𝑔 𝑥 = 𝑓(𝑥) ∙ 𝑔(𝑥) Multiplication 𝑓 𝑔 𝑥 = 𝑓(𝑥)/𝑔 𝑥 Division 𝑓 ∘ 𝑔 𝑥 = 𝑓(𝑔 𝑥 ) Composition
- 7. Operations on Functions Examples: 1. Given 𝑓 𝑥 = 3𝑥 + 2 and 𝑔 𝑥 = 4 − 5𝑥, Find: i. (𝑓 + 𝑔)(𝑥) ii. 𝑓 − 𝑔 𝑥 iii. 𝑓 ∙ 𝑔 𝑥 iv. 𝑓 𝑔 𝑥
- 8. Operations on Functions Examples: 2. Given: 𝑓 𝑥 = 2𝑥, 𝑔 𝑥 = 𝑥 + 4, and ℎ 𝑥 = 5 − 𝑥3 . Find: i. 𝑓 + 𝑔 2 ii. ℎ − 𝑔 2 iii. 𝑓 ∙ ℎ 2 iv. ℎ 𝑔 2 v. (𝑔 ∘ ℎ)(2)
- 9. Drills For numbers 5 and 6, evaluate the following functions. 5. Given the function 𝑓 𝑥 = 5𝑥 + 8, find the value of the output given the following input or argument a. 𝑓 𝑡 b. 𝑓 −8 c. 𝑓 5 d. 𝑓 3𝑥 e. 𝑓(7 − 𝑥)
- 10. Functions in Real-Life Situations Example 1: f(t) = 10,000(1.05)t represent the amount of money if P10,000 is invested at 5% compounded annually. Example 2: Suppose that a jeepney ride costs P8 for the first 4 kilometers, then an additional P1.50 for each succeeding kilometer.Then the cost of a jeepney fare for a jeepney on an 8-kilometer route can be modeled by: 𝐹( 𝑑) = 8.00 𝑖𝑓 0 < 𝑑 ≤ 4 9.50 𝑖𝑓 4 < 𝑑 ≤ 5 11.00 𝑖𝑓 5 < 𝑑 ≤ 6 12.50 𝑖𝑓 6 < 𝑑 ≤ 7 14.00 𝑖𝑓 7 < 𝑑 ≤ 8 where d is the distance travelled and F(d) is the fare.
- 11. Piecewise Function • Is a function defined by multiple sub-functions with each sub- function applying to a certain interval of the function’s domain (or a sub-domain) 𝐹( 𝑑) = 8.00 𝑖𝑓 0 < 𝑑 ≤ 4 9.50 𝑖𝑓 4 < 𝑑 ≤ 5 11.00 𝑖𝑓 5 < 𝑑 ≤ 6 12.50 𝑖𝑓 6 < 𝑑 ≤ 7 14.00 𝑖𝑓 7 < 𝑑 ≤ 8
- 12. Piecewise Function Example: •The fee for hiring a guide to hike Mt. Apo is P700. Suppose that the guide can take care of at least 8 hikers and a maximum of 16. For every succeeding 2 hikers, there is an additional fee of P125. Represent the cost of hiring guides as a piecewise function of the number of hikers.
- 13. REVIEWTHE CONCEPTS FOR A SMOOTH FLOWTHISWEEK! :3