In exercises 1 4 identify each function as a constant...

In Exercises $1-4,$ identify each function as a constant function, linear function, power function, polynomial (state its degree), rational function, algebraic function, trigonometric function, exponential function, or logarithmic function. Remember that some functions can fall into more than one category. $$ \begin{array}{ll}{\text { a. } f(x)=7-3 x} & {\text { b. } g(x)=\sqrt[5]{x}} \\ {\text { c. } h(x)=\frac{x^{2}-1}{n^{2}+1}} & {\text { d. } r(x)=8^{x}}\end{array} $$

Transcript

00:01 This question we have to identify each as a constant, whether it's a constant, linear, power, polynomial, rational, algebraic, trigonometric, exponential, or logarithmic function.

00:12 In which list, so let's go one by one.

00:14 So we have fx is equal to 7 minus 3x.

00:17 So that's pretty much intuitive, right? any any function of the form a x plus b is always categorized as a linear function.

00:27 So we're going to say that this is a linear function.

00:30 Linear function option option b is g x is equal to x raised to 1 over 5 it's not a constant it's not a linear is that a power function and not really because power function as is of the type a raise to x a polynomial has a integral sorry the the powers are always whole numbers or no rational function no algebra yes this is an algebraic function and it's not a trigonometry is not an exponential it's not an exponential as as well because the exponential has a power in the in the as a variable and we have it's not even a logarithmic function as well so it's a algebra function for sure and it's also a power function because power function is a variable raised to a a real constant number so we're going to say that it's a power function and it's an algebra function as well because the algebra function are the roots of the polynomial function uh c is x square minus one or n square plus one so uh this is not a constant not a linear not a power function but this is in fact uh let's see it's it's a rational it's a polynomial for sure because n squared plus one is a constant and it's a constant so i'm going to say that this is a polynomial function and degree is two it's a rational function as well it's a rational function as well because a denominator can just be regarded as a constant so anyway that's a rational function and uh it's not an algebraic not a trigromatic not an exponential, not a logarithmic function as well.

02:34 And over here, let's see if there anyone fits...

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