Question 1

State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not.
-$$f ( x ) = 3 - \frac { 1 } { 3 } x$$
A) Yes; degree 1
B) No; x has a fractional coefficient
C) Yes; degree 3
D) Yes; degree 0

Accepted Answer

The function is a polynomial because it can be written in the form $ax + b$, where $a$ and $b$ are constants. The highest power of $x$ is 1, so its degree is 1.

Question 2

f(x) = (x + 2)⁵ + 4 A) B) C) D)

Accepted Answer

C

Question 3

State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not. -f(x) = 4x + 2x³ A) Yes; degree 3 B) Yes; degree 2 C) Yes; degree 1 D) Yes; degree 4

Accepted Answer

The function f(x) = 4x + 2x^3 is a polynomial function because it is a sum of terms with non-negative integer exponents. The degree of the polynomial is the highest exponent, which is 3.

Question 4

State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not.
-$$f ( x ) = \frac { 2 - x ^ { 2 } } { 5 }$$
A) No; x is a negative term
B) Yes; degree 2
C) Yes; degree 1
D) No; it is a ratio

Accepted Answer

The function is a polynomial because it can be simplified to $-\frac{1}{5}x^2 + \frac{2}{5}$, which is a polynomial of degree 2.

Question 5

f(x) = (x + 5)⁵ A) B) C) D)

Accepted Answer

The answer of f(x) = (x + 5)⁵ A) B) C) D) ...

Question 6

A)

B)

C)

D)

Accepted Answer

The answer of  
A)

B)

C)

D)
...

Question 7

State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not. -f(x) = 19x⁵ + 9x⁴ + 2 A) Yes; degree 9 B) No; the last term has no variable C) Yes; degree 10 D) Yes; degree 5

Accepted Answer

The function is a polynomial function because it is a sum of terms with non-negative integer exponents. The degree of the polynomial is the highest exponent, which is 5.

Question 8

f(x) = x⁵ + 4 A) B) C) D)

Accepted Answer

The answer of f(x) = x⁵ + 4 A) B) C) D) ...

Question 9

$f ( x ) = \frac { 1 } { 2 } ( x + 2 ) ^ { 4 } + 2$
 
A)

B)

C)

D)

Accepted Answer

The answer of \(f ( x ) = \frac {...

Question 10

A)

B)

C)

D)

Accepted Answer

The answer of  
A)

B)

C)

D)
...

Question 11

A)

B)

C)

D)

Accepted Answer

The answer of  
A)

B)

C)

D)

...

Question 12

f(x) = (x - 3)4 + 4  
A)

B)

C)

D)

Accepted Answer

The answer of f(x) = (x - 3)4 + 4...

Question 13

$f ( x ) = \frac { 1 } { 2 } ( x - 3 ) ^ { 5 } + 2$

A)

B)

C)

D)

Accepted Answer

The answer of \(f ( x ) = \frac {...

Question 14

A)

B)

C)

D)

Accepted Answer

The answer of  
A)

B)

C)

D)
...

Question 15

State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not.
-$$f ( x ) = 1 + \frac { 7 } { x }$$
A) Yes; degree 7
B) Yes; degree 0
C) Yes; degree 1
D) No; x is raised to a negative power

Accepted Answer

The function is not a polynomial because it contains $x$ raised to a negative power ($\frac{1}{x} = x^{-1}$). Polynomial functions only include terms where the variable is raised to a non-negative integer power.

Question 16

f(x)=5x⁵ A) B) C) D)

Accepted Answer

The answer of f(x)=5x⁵ A) B) C) D) ...

Question 17

State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not.
-f(x) = x(x - 9)
A) Yes; degree 1
B) Yes; degree 2
C) Yes; degree 0
D) No; it is a product

Accepted Answer

The function f(x) = x(x - 9) is a polynomial function because it can be simplified to $x^2 - 9x$, which is a polynomial of degree 2.

Question 18

f(x) = 3 - (x - 4)⁴ A) B) C) D)

Accepted Answer

The answer of f(x) = 3 - (x - 4)<sup>4...

Question 19

f(x) = -2(x - 5)⁴ + 3 A) B) C) D)

Accepted Answer

The answer of f(x) = -2(x - 5)⁴ + 3...

Question 20

State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not.
-f(x) = 15
A) No; it contains no variables
B) No; it is a constant
C) Yes; degree 1
D) Yes; degree 0

Accepted Answer

The function f(x) = 15 is a polynomial function. It is considered a constant polynomial, and its degree is 0 because it does not contain any variables raised to a power.

Quiz 3: Polynomial and Rational Functions

State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not. - $f ( x ) = 3 - \frac { 1 } { 3 } x$

f(x) = (x + 2) ⁵ + 4

State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not. -f(x) = 4x + 2x³

State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not. - $f ( x ) = \frac { 2 - x ^ { 2 } } { 5 }$

f(x) = (x + 5) ⁵

State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not. -f(x) = 19x⁵ + 9x⁴ + 2

f(x) = x⁵ + 4

$f ( x ) = \frac { 1 } { 2 } ( x + 2 ) ^ { 4 } + 2$ $f ( x ) = \frac { 1 } { 2 } ( x + 2 ) ^ { 4 } + 2 A) B) C) D)$

f(x) = (x - 3) 4 + 4

$f ( x ) = \frac { 1 } { 2 } ( x - 3 ) ^ { 5 } + 2$ $f ( x ) = \frac { 1 } { 2 } ( x - 3 ) ^ { 5 } + 2 A) B) C) D)$

State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not. - $f ( x ) = 1 + \frac { 7 } { x }$

f(x) =5x⁵

State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not. -f(x) = x(x - 9)

f(x) = 3 - (x - 4) ⁴

f(x) = -2(x - 5) ⁴ + 3

State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not. -f(x) = 15

Quiz 3: Polynomial and Rational Functions

State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not. - f(x) =3−13xf ( x ) = 3 - \frac { 1 } { 3 } xf(x) =3−31​x

f(x) = (x + 2) 5 + 4

State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not. -f(x) = 4x + 2x3

State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not. - f(x) =2−x25f ( x ) = \frac { 2 - x ^ { 2 } } { 5 }f(x) =52−x2​

f(x) = (x + 5) 5

State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not. -f(x) = 19x5 + 9x4 + 2

f(x) = x5 + 4

f(x) =12(x+2) 4+2f ( x ) = \frac { 1 } { 2 } ( x + 2 ) ^ { 4 } + 2f(x) =21​(x+2) 4+2

f(x) = (x - 3) 4 + 4

f(x) =12(x−3) 5+2f ( x ) = \frac { 1 } { 2 } ( x - 3 ) ^ { 5 } + 2f(x) =21​(x−3) 5+2

State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not. - f(x) =1+7xf ( x ) = 1 + \frac { 7 } { x }f(x) =1+x7​

f(x) =5x5

State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not. -f(x) = x(x - 9)

f(x) = 3 - (x - 4) 4

f(x) = -2(x - 5) 4 + 3

State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not. -f(x) = 15

State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not. - $f ( x ) = 3 - \frac { 1 } { 3 } x$

f(x) = (x + 2) ⁵ + 4

State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not. -f(x) = 4x + 2x³

State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not. - $f ( x ) = \frac { 2 - x ^ { 2 } } { 5 }$

f(x) = (x + 5) ⁵

State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not. -f(x) = 19x⁵ + 9x⁴ + 2

f(x) = x⁵ + 4

$f ( x ) = \frac { 1 } { 2 } ( x + 2 ) ^ { 4 } + 2$ $f ( x ) = \frac { 1 } { 2 } ( x + 2 ) ^ { 4 } + 2 A) B) C) D)$

$f ( x ) = \frac { 1 } { 2 } ( x - 3 ) ^ { 5 } + 2$ $f ( x ) = \frac { 1 } { 2 } ( x - 3 ) ^ { 5 } + 2 A) B) C) D)$

State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not. - $f ( x ) = 1 + \frac { 7 } { x }$

f(x) =5x⁵

f(x) = 3 - (x - 4) ⁴

f(x) = -2(x - 5) ⁴ + 3