How are rational functions similar to linear, quadratic, or exponential functions? How are they different? When are these similarities or differences important when looking for intersections between rational functions and other types of functions? Be sure to cite examples as you explain your ideas.

See explanation below for further details.

Step-by-step explanation:

A rational consist of two real numbers such that:

If c is a polynomial with a certain grade, then, both the numerator and the denominator must be also polynomials and the grade of the numerator must be greater than denominator.

If c is linear function, that is, a first order polynomial, then a must be a (n+1)-th polynomial and b must be a n-th polynomial.

Example:

If and , then:

If c is a quadratic function, that is, a second order polynomial, then a must be a (n+1)-th polynomial and b must be a n-th polynomial.

Example

If and , then:

But if c is an exponential, both the numerator and the denominator must be therefore exponential function and grade of each exponential function must different to the other.

Example

If and , then:

Otherwise, c would be equal to a constant function, that is, a polynomial with a grade 0.

If and , then:

Example

It is worth to add that exponential functions can be a linear combination of single exponential function, similar to polynomials.

Example

its c or d   take a lucky guess my dude

answer:

it is general formula that is used to write value to its excet position

a11 a12 a13

a21 a22 a23

it is the example of order 2 by 3 matrix in this

a11 means value occur in 1 st row 1st column

a12 means value occurs in 1st row 2nd column

a13 means value occur in 1st row and 3rd column

a21 means value occurs in 2nd row and 1st column

a22 means value occurs in 2nd row and in 2nd column

a23 means value occurs in 2nd row and in 3rd column