Q. 2 TB - Calculus

Question

What is a monomial? What is a power function? What is a polynomial? What is a rational function?

Step-by-Step Solution

Answer

Monomial: monomial is a single non-zero term algebraic expression that consists of a number, variable, or variable with its coefficient and its degree. 

Power function: A power function is a single term function that consists of a coefficient with a variable having an exponent of numeric value. 

Polynomial: polynomial is an algebraic expression formed by the algebraic operation between terms except division and terms consist of a number, variable, or variable with its coefficient and its degree. 

Rational function: A function that is formed by a ratio of two polynomial functions where the denominator polynomial function cannot be zero. 

Step 1. Given information.

The topics that need to describe are the followings.

• monomial 
• power function 
• polynomial 
• rational function 

Step 2. monomial.

Monomial: monomial is a single non-zero term algebraic expression that consists of a number, variable, or variable with its coefficient and its degree.

Examples: $5,x, 2y, 3x^2$

Exponents of variables in monomial cannot be negative.

The monomial can't consist of a variable in the Denominator.

Step 3. power function

Power function: A power function is a single term function that consists of a coefficient with a variable having an exponent of numeric value.

The standard form of a power function is $f\left(x\right)=a{x}^p$

where a is the coefficient, x is the variable, and p is the numeric value exponent.

Example:$f\left(x\right)=2x^3$

Step 4. Polynomial.

Polynomial: polynomial is an algebraic expression formed by the algebraic operation between terms except division and terms consist of a number, variable, or variable with its coefficient and its degree.

Examples: $4y^2-3y+2$

Exponents of variables in monomial cannot be negative.

The monomial can't consist of a variable in the Denominator.

Step 5. rational function

Rational function: A function that is formed by a ratio of two polynomial functions where the denominator polynomial function cannot be zero.

The standard form of a rational function is $f\left(x\right)=\frac{p\left(x\right)}{q\left(x\right)}$

where $p\left(x\right) \& q\left(x\right)$are polynomials and $q\left(x\right)\ne 0.$

Example:$f\left(x\right)=\frac{x^2+2x+3}{x+3}$