Determining if polynomial function

In summary, the conversation discusses the concept of polynomial functions and how they are defined as functions with positive integer exponents and any coefficients, not just rational numbers. The examples given (a), d), and g)) are not polynomial functions because they contain negative or fractional exponents. The conversation also touches on the properties of exponents, specifically the one that states that a negative exponent can be written as a fraction with the base raised to the positive exponent. It is important to understand these properties in order to correctly evaluate expressions with exponents.
  • #1
Nelo
215
0

Homework Statement



We know that a polynomial function is anything with a positive exponent and a rational number.

a) - / x^3 -4


d) 3x^-1 - 11

g) y= [sqrt of term]3x^2 -5x


Homework Equations





The Attempt at a Solution



c) 1 / x^3 - 4
(do we use exponents to verify ?)
i
e) 1^1 / x^3 -4^1
1-3 = -2 , 1-1 = 0
Therefore there is a negetive exponent on the x^3, is that why?

4d) y= 3^x-1 - 11
(how do u know this isnt?)

g) [sqrtofentireterm] 3x^3-5x

Why is that not a polynomial function?

Thnx 4 the help!
 
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  • #2
Nelo said:

Homework Statement



We know that a polynomial function is anything with a positive exponent and a rational number.
No, we don't know that! That is wrong. A polynomial function can has the variable, x, only to positive integer exponents. The coefficients can be any numbers, not just rational numbers.

a) - / x^3 -4
what does the "-/" mean? Is that an attempt at a squareroot symbol? Better would be "sqrt(x^3- 4) which is the same as (x^3- 4)^(1/2). That's not a polynomial because it has a fractional exponent.

d) 3x^-1 - 11
negative exponent

g) y= [sqrt of term]3x^2 -5x
again, sqrt= exponent 1/2.

Homework Equations





The Attempt at a Solution



c) 1 / x^3 - 4
(do we use exponents to verify ?)
is that 1/(x^3- 4) or (1/x^3)- 4?
In either case, there is a negative exponent, (x^3- 4)^(-1) or x^(-3)- 4.

e) 1^1 / x^3 -4^1
1-3 = -2 , 1-1 = 0
I hav no clue what you are doing here.

Therefore there is a negetive exponent on the x^3, is that why?

4d) y= 3^x-1 - 11
(how do u know this isnt?)
3^(x- 1) does not have x to a power.

g) [sqrtofentireterm] 3x^3-5x

Why is that not a polynomial function?
Again, because of the square root= 1/2 power.

Thnx 4 the help!
 
  • #3
Therefore there is a negetive exponent on the x^3, is that why?

4d) y= 3^x-1 - 11
(how do u know this isnt?)

3^(x- 1) does not have x to a power

Why do you mean does not have x to a power??


c) 1 / x^3 - 4
(do we use exponents to verify ?)

is that 1/(x^3- 4) or (1/x^3)- 4?
In either case, there is a negative exponent, (x^3- 4)^(-1) or x^(-3)- 4.

How is there a negetive exponent there... how do u verify? There is no braackets anywhere on my page so i wrote it as written. Do u evalue the exponents in the divsion and then it comes out as a negetive exponent?
 
  • #4
Nelo said:
How is there a negetive exponent there... how do u verify? There is no braackets anywhere on my page so i wrote it as written. Do u evalue the exponents in the divsion and then it comes out as a negetive exponent?
Do you know the properties of exponents? Specifically, this one:
[tex]a^{-n} = \frac{1}{a^n}, a \ne 0[/tex]
If not, you'll need to review them.
 

FAQ: Determining if polynomial function

What is a polynomial function?

A polynomial function is a mathematical expression that consists of one or more variables raised to non-negative integer powers. It can also include coefficients and constants, and is often written in the form of ax^n + bx^(n-1) + ... + cx + d.

How do you determine if a function is a polynomial function?

To determine if a function is a polynomial function, you must check if the exponents on the variables are all non-negative integers and if there are no variables in the denominator. The function must also have a constant term (a value with no variable). If all of these conditions are met, then the function is a polynomial function.

What is the degree of a polynomial function?

The degree of a polynomial function is the highest exponent on the variable in the function. For example, the degree of the function 5x^3 + 2x^2 + 1 is 3 because the highest exponent is 3. The degree of a polynomial function can also tell you the number of solutions the function may have.

How do you solve for the roots of a polynomial function?

To solve for the roots of a polynomial function, you must set the function equal to zero and use algebraic methods to find the values of the variable(s) that make the equation true. These values are the roots or solutions of the polynomial function.

What are some real-life applications of polynomial functions?

Polynomial functions are used in various fields such as engineering, physics, economics, and statistics. They can be used to model and analyze relationships between variables, make predictions and projections, and solve real-world problems. Some examples of real-life applications of polynomial functions include calculating projectile motion, determining population growth, and analyzing financial data.

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