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Mathway |Algebra Problem Solver
Analyzing Poly Functions
Question 1 of 8 (1 point) | Question Attempt: 2 of Unlimited
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For each function, determine whether it is a polynomial function.

Is the function a polynomial?

(a)
v(x)=1-(5)/(x)
Yes

(b)
h(x)=6x^(-3)+5x
0

(c)
f(x)=-3sqrtx

(d)
g(x)=4(x-4)(x+2)

Check

Clever | Portal $\newline$ Mathway |Algebra Problem Solver $\newline$ Analyzing Poly Functions $\newline$ Question $1$ of $8$ ( $1$ point) | Question Attempt: $2$ of Unlimited $\newline$ $1$ $\newline$ $2$ $\newline$ $3$ $\newline$ $4$ $\newline$ $5$ $\newline$ $6$ $\newline$ $7$ $\newline$ For each function, determine whether it is a polynomial function. $\newline$ \begin{tabular}{|l|l|} $\newline$ \hline & Is the function a polynomial? \\ $\newline$ \hline (a) $v(x)=1-\frac{5}{x}$ & Yes \\ $\newline$ \hline (b) $h(x)=6 x^{-3}+5 x$ & $0$ \\ $\newline$ \hline (c) $f(x)=-3 \sqrt{x}$ & \\ $\newline$ \hline (d) $g(x)=4(x-4)(x+2)$ & \\ $\newline$ \hline $\newline$ \end{tabular} $\newline$ Check

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Function transformation rules

Full solution

Q. Clever | Portal

\newline

Mathway |Algebra Problem Solver

\newline

Analyzing Poly Functions

\newline

Question

1

of

8

(

1

point) | Question Attempt:

2

of Unlimited

\newline

1

\newline

2

\newline

3

\newline

4

\newline

5

\newline

6

\newline

7

\newline

For each function, determine whether it is a polynomial function.

\newline

\begin{tabular}{|l|l|}

\newline

\hline & Is the function a polynomial? \\

\newline

\hline (a)

v(x)=1-\frac{5}{x}

& Yes \\

\newline

\hline (b)

h(x)=6 x^{-3}+5 x

&

0

\\

\newline

\hline (c)

f(x)=-3 \sqrt{x}

& \\

\newline

\hline (d)

g(x)=4(x-4)(x+2)

& \\

\newline

\hline

\newline

\end{tabular}

\newline

Check

Check for Polynomial: For $(a) v(x) = 1 - (5/x)$ , check if it's a polynomial. Polynomials can't have negative or fractional exponents, nor variables in the denominator. Since $v(x)$ has $x$ in the denominator, it's not a polynomial.
Identify Non-Polynomial: For $(b) h(x) = 6x^{(-3)} + 5x$ , check if it's a polynomial. $h(x)$ has a term with a negative exponent, which is not allowed in polynomials. So, $h(x)$ is not a polynomial.
Check for Polynomial: For $(c) f(x) = -3\sqrt{x}$ , check if it's a polynomial. Polynomials can't have variables under a radical. Since $f(x)$ has a square root of $x$ , it's not a polynomial.
Identify Non-Polynomial: For $(d) g(x) = 4(x-4)(x+2)$ , check if it's a polynomial. $\newline$ This function is written as a product of linear factors, which is a characteristic of polynomials. $\newline$ So, $g(x)$ is a polynomial.

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