Table of Contents
Introduction to Common Functions
A function is a set of instructions that can be used to carry out a specific task. Functions are commonly used in computer programs to carry out specific tasks.
Some common functions that are used in computer programs include:
-Printing text
-Inputting text
-Inputting numbers
-Outputting numbers
-Calculating values
-Checking for errors
-Performing calculations
-Sorting data
-Searching data
-Retrieving data from a database
Meaning of GCD
The greatest common divisor (GCD) of two or more numbers is the largest number that divides evenly into each of the numbers. The GCD is also the smallest positive number that is divisible by each of the numbers.
GCD OF Negative Numbers
The greatest common divisor (GCD) of two or more negative integers is the largest positive integer that divides each of them without leaving a remainder. For example, the GCD of -8 and -6 is 2, because 2 is the largest positive integer that divides -8 and -6 without leaving a remainder.
GCD of Polynomial
The GCD of two polynomials is the largest polynomial that can be divided by both of them without remainder.
GCD of Polynomial Example
The GCD of a polynomial is the polynomial that is the smallest degree and has the same coefficients as the given polynomial.
For example, the GCD of 4×3 – 5×2 + 3x – 2 and 6×3 – 7×2 + 5x – 4 is 3×2 – 2x + 1.
LCM of Polynomial
Functions
The least common multiple (LCM) of two or more polynomial functions is the smallest polynomial that is divisible by each of the given functions.
To find the LCM of two or more polynomial functions, use the following steps:
1. Factor each of the given polynomial functions.
2. Write the LCM as the product of all of the factors that are common to all of the given functions.
3. Cancel any factors that are common to more than one of the given functions.
4. Simplify the LCM if possible.
Here is an example:
Find the LCM of the following functions:
x3 + 2×2 – 5x + 6
x3 – 2×2 + 5x – 6
The LCM of the given functions is x3 – 2×2 + 5x – 6.
Quadratic Function
A quadratic function is a polynomial function in the form where and are real numbers and is a non-negative integer. The graph of a quadratic function is a parabola.
Common Roots of Quadratic Functions Conditions
for Quadratic Functions
There are three conditions that must be satisfied in order for a function to be a quadratic function.
1. The function must have the form y = ax2 + bx + c, where a, b, and c are real numbers.
2. The function must be differentiable at all points in its domain.
3. The function must have a unique solution for all x values in its domain.
Example
What are the odds of flipping a coin and getting heads?
The odds of flipping a coin and getting heads are 1 in 2.
Common Trigonometric Functions
There are six basic trigonometric functions: sine, cosine, tangent, cotangent, secant, and cosecant.
The sine, cosine, and tangent functions are defined as ratios of two sides of a right triangle:
The cosecant, secant, and cotangent functions are defined as reciprocals of the sine, cosine, and tangent functions:
The following table summarizes the basic trigonometric functions:
Common Trig Angles
There are six basic trigonometric angles:
0 degrees, 30 degrees, 45 degrees, 60 degrees, 90 degrees, and 120 degrees.
Solved Example
Question
A student is trying to solve the equation 3x + 5 = 7. She knows that 3x + 5 = 12 and 3x = 7. What is the value of x?
x = 2
