Question

Explain the types of Algebric functions
with examples
​

Answer 1

Answer:

An algebraic function is a function that involves only algebraic operations, like, addition, subtraction, multiplication, and division, as well as fractional or rational exponents. ... There are many different types of algebraic functions: linear, quadratic, cubic, polynomial, rational, and radical equations.

Step-by-step explanation:

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Answer 2

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Algebraic Functions

• A function is called an algebraic function if it can be constructed using algebraic operations (such as
• addition, subtraction, multiplication, division and taking roots).

• Polynomials, power functions, and rational function are all algebraic functions.

1 Polynomials

• A function p is a polynomial if

[tex]p(x) = anx

n + an−1x

n−1 + ... + a2x

2 + a1x + a0[/tex]

• where n is a nonnegative integer and a0, a1, a2, ..., an−1, an are all constants called coefficients of the
• polynomial.
• If the leading coefficient an 6= 0 then the degree of p(x) is n.

• A polynomial of degree 1 is called a linear function.

• A polynomial of degree 2 is called a quadratic function.

• A polynomial of degree 3 is called a cubic function.

• A polynomial of degree 4 is called a quartic function.

• A polynomial of degree 5 is called a quintic function.

• ...and so on...

• We often talk about finding roots of a polynomial. This means we are finding where the graph of the

function hits the x-axis. Finding the roots of a polynomial entails setting the polynomial equal to zero and

solving for x.

[tex]Find \: the \: roots \: of \: p(x) = x

2 − x − 6.[/tex]

Linear Functions

• The most famous polynomial is the linear function.
• y is said to be a linear function of x if the graph of the function is a line so that we can use the
• slope-intercept form of the equation of a line to write a formula for the function as

y = mx + b

• where m is the slope and b is the y-intercept.
• If this is the case, what do m and b equal in the p(x) equation?
• Graph the family of equations f(x) = x+b where be is an integer b = −2, −1, 0, 1, 2 on the same coordinate
• system.
• Graph the family of equations f(x) = mx where be is an integer m = −2, −1, 0, 1, 2 on the same coordinate
• system.
• Find the equation for a line that passes through (2, −1) and (3, 5).

2 Power Functions

• A function of the form f(x) = x
• a where a is a constant is called a power function. The power function
• takes a variety of forms based on the type of constant that a is.
• These different forms arrise wheη

• 2.1 a = n where is n a positive integer,

• 2.2 a = 1/n where n is a positive integer, and

• 2.3 a = −1.

• We will explore these forms in the following sections.

$hope \: its \: help \: u$