Question 1

State whether the function is a polynomial function or not. If it is, give its degree.

-$$f ( x ) = x ^ { 4 / 3 } - x ^ { 5 } + 5$$
A) Yes; degree $4 / 3$
B) Yes; degree 4
C) Not a polynomial
D) Yes; degree 5

Accepted Answer

A polynomial function must have non-negative integer exponents. The term $x^{4/3}$ has a fractional exponent, so $f(x)$ is not a polynomial function.

Question 2

Use the graph of a power function and transformations to sketch the graph of the polynomial function.

-$$( x ) = 3 - ( x + 2 ) ^ { 4 }$$

A)

B)

C)

D)

Accepted Answer

The answer of Use the graph of a power function...

Question 3

State whether the function is a polynomial function or not. If it is, give its degree.

-$$f ( x ) = \frac { 6 - x ^ { 3 } } { 6 }$$
A)Yes; degree 1
B)Not a polynomial
C)Yes; degree 3
D)Yes; degree 6

Accepted Answer

The function is a polynomial because it can be simplified to $f(x) = -\frac{1}{6}x^3 + 1$, which is a polynomial in standard form. Its highest degree term is $x^3$, so its degree is 3.

Question 4

Use the graph of a power function and transformations to sketch the graph of the polynomial function.

- 
A)

B)

C)

D)

Accepted Answer

The answer of Use the graph of a power function...

Question 5

Use the graph of a power function and transformations to sketch the graph of the polynomial function.

-$$f ( x ) = ( x + 5 ) ^ { 4 } + 3$$

A)

B)

C)

D)

Accepted Answer

The answer of Use the graph of a power function...

Question 6

Solve the problem.
-You have 80 feet of fencing to enclose a rectangular region. What is the maximum area? 
A) $6400 \mathrm { ft } ^ { 2 }$
B) $400 \mathrm { ft } ^ { 2 }$
C) $1600 \mathrm { ft } ^ { 2 }$
D) $396 \mathrm { ft } ^ { 2 }$

Accepted Answer

The maximum area enclosed by a given perimeter is achieved with a square. The perimeter of a square is $4s$, where $s$ is the side length. Given a perimeter of 80 feet, each side is $80 \div 4 = 20$ feet. The area is $20^2 = 400 \, \mathrm{ft}^2$.

Question 7

State whether the function is a polynomial function or not. If it is, give its degree.

-$$f ( x ) = 1 - \frac { 1 } { 5 } x$$
A)Yes; degree 1
B)Yes; degree 5
C)Not a polynomial
D)Yes; degree 0

Accepted Answer

The function $f(x) = 1 - \frac{1}{5}x$ is a polynomial because it can be written in the form $a_nx^n + a_{n-1}x^{n-1} + \cdots + a_1x + a_0$, where $n$ is a non-negative integer and the coefficients $a_n, a_{n-1}, \ldots, a_0$ are constants. In this case, the highest power of $x$ is 1, so the degree of the polynomial is 1.

Question 8

State whether the function is a polynomial function or not. If it is, give its degree.

-$$f ( x ) = 3 x + 7 x ^ { 4 }$$
A)Yes; degree 4
B)Yes; degree 3
C)Yes; degree 7
D)Yes; degree 1

Accepted Answer

The function $f(x) = 3x + 7x^4$ is a polynomial because it is a sum of monomials (terms of the form $ax^n$, where $a$ is a coefficient and $n$ is a non-negative integer). The highest power of $x$ in the function is 4, so the degree of the polynomial is 4.

Question 9

State whether the function is a polynomial function or not. If it is, give its degree.

-$$f ( x ) = \frac { x ^ { 4 } - 7 } { x ^ { 5 } }$$
A)Yes; degree 5
B)Not a polynomial
C)Yes; degree -5
D)Yes; degree 4

Accepted Answer

The given function $f(x) = \frac{x^4 - 7}{x^5}$ is not a polynomial because it involves division by a variable, which can result in terms that are not non-negative integer powers of that variable.

Question 10

Use the graph of a power function and transformations to sketch the graph of the polynomial function.

-$$f ( x ) = ( x - 4 ) ^ { 4 }$$

A)

B)

C)

D)

Accepted Answer

The answer of Use the graph of a power function...

Question 11

Use the graph of a power function and transformations to sketch the graph of the polynomial function.

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

A)

B)

C)

D)

Accepted Answer

The answer of Use the graph of a power function...

Question 12

Use the graph of a power function and transformations to sketch the graph of the polynomial function.

- 
A)

B)

C)

D)

Accepted Answer

The answer of Use the graph of a power function...

Question 13

Use the graph of a power function and transformations to sketch the graph of the polynomial function.

- 
A)

B)

C)

D)

Accepted Answer

The answer of Use the graph of a power function...

Question 14

Solve the problem.
-You have 76 feet of fencing to enclose a rectangular plot that borders on a river. If you do not fence the side along the river, find the length and width of the plot that will maximize the area.
A)length: 38 ft, width: 38 ft
B)length: 57 ft, width: 19 ft
C)length: 19 ft, width: 19 ft
D)length: 38 ft, width: 19 ft

Accepted Answer

To maximize the area of a rectangle when one side (the length along the river) is not fenced, you use the fencing for the two widths and one length. Let the width be $w$ and the length be $l$. You have $2w + l = 76$. To maximize the area ($A = w \times l$), set $l = 76 - 2w$, and substitute into the area formula to get $A = w(76 - 2w)$. The maximum area occurs when $w = 19$ ft (by setting the derivative of the area function to zero or using symmetry), making the length $l = 76 - 2(19) = 38$ ft.

Question 15

Use the graph of a power function and transformations to sketch the graph of the polynomial function.

- 
A)

B)

C)

D)

Accepted Answer

The answer of Use the graph of a power function...

Question 16

State whether the function is a polynomial function or not. If it is, give its degree.

-$$f ( x ) = 12 x ^ { 4 } - 2 x ^ { 3 } + 2$$
A)Yes; degree 7
B)Not a polynomial
C)Yes; degree 4
D)Yes; degree 8

Accepted Answer

The function $f(x) = 12x^4 - 2x^3 + 2$ is a polynomial because it is a sum of monomials (terms of the form $ax^n$, where $a$ is a coefficient and $n$ is a non-negative integer). The highest power of $x$ in the function is 4, so its degree is 4.

Question 17

State whether the function is a polynomial function or not. If it is, give its degree.

-f(x)= 6
A)Yes; degree 1
B)Yes; degree 0
C)Not a polynomial
D)Yes; degree 6

Accepted Answer

The function $f(x) = 6$ is a polynomial function, specifically a constant function. The degree of a constant non-zero polynomial is 0.

Question 18

Use the graph of a power function and transformations to sketch the graph of the polynomial function.

-$$f ( x ) = \frac { 1 } { 2 } ( x + 3 ) ^ { 4 } + 2$$

A)

B)

C)

D)

Accepted Answer

The answer of Use the graph of a power function...

Question 19

Use the graph of a power function and transformations to sketch the graph of the polynomial function.

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

A)

B)

C)

D)

Accepted Answer

The answer of Use the graph of a power function...

Question 20

Use the graph of a power function and transformations to sketch the graph of the polynomial function.

- 
A)

B)

C)

D)

Accepted Answer

The answer of Use the graph of a power function...

Quiz 4: Polynomial and Rational Functions

State whether the function is a polynomial function or not. If it is, give its degree. - $f ( x ) = x ^ { 4 / 3 } - x ^ { 5 } + 5$

Use the graph of a power function and transformations to sketch the graph of the polynomial function. - $( x ) = 3 - ( x + 2 ) ^ { 4 }$ $Use the graph of a power function and transformations to sketch the graph of the polynomial function. - ( x ) = 3 - ( x + 2 ) ^ { 4 } A) B) C) D)$

State whether the function is a polynomial function or not. If it is, give its degree. - $f ( x ) = \frac { 6 - x ^ { 3 } } { 6 }$

Use the graph of a power function and transformations to sketch the graph of the polynomial function. -

Use the graph of a power function and transformations to sketch the graph of the polynomial function. - $f ( x ) = ( x + 5 ) ^ { 4 } + 3$ $Use the graph of a power function and transformations to sketch the graph of the polynomial function. - f ( x ) = ( x + 5 ) ^ { 4 } + 3 A) B) C) D)$

Solve the problem. -You have 80 feet of fencing to enclose a rectangular region. What is the maximum area?

State whether the function is a polynomial function or not. If it is, give its degree. - $f ( x ) = 1 - \frac { 1 } { 5 } x$

State whether the function is a polynomial function or not. If it is, give its degree. - $f ( x ) = 3 x + 7 x ^ { 4 }$

State whether the function is a polynomial function or not. If it is, give its degree. - $f ( x ) = \frac { x ^ { 4 } - 7 } { x ^ { 5 } }$

Use the graph of a power function and transformations to sketch the graph of the polynomial function. - $f ( x ) = ( x - 4 ) ^ { 4 }$ $Use the graph of a power function and transformations to sketch the graph of the polynomial function. - f ( x ) = ( x - 4 ) ^ { 4 } A) B) C) D)$

Use the graph of a power function and transformations to sketch the graph of the polynomial function. -

Use the graph of a power function and transformations to sketch the graph of the polynomial function. -

Solve the problem. -You have 76 feet of fencing to enclose a rectangular plot that borders on a river. If you do not fence the side along the river, find the length and width of the plot that will maximize the area.

Use the graph of a power function and transformations to sketch the graph of the polynomial function. -

State whether the function is a polynomial function or not. If it is, give its degree. - $f ( x ) = 12 x ^ { 4 } - 2 x ^ { 3 } + 2$

State whether the function is a polynomial function or not. If it is, give its degree. -f(x) = 6

Use the graph of a power function and transformations to sketch the graph of the polynomial function. -

Quiz 4: Polynomial and Rational Functions

State whether the function is a polynomial function or not. If it is, give its degree. - f(x) =x4/3−x5+5f ( x ) = x ^ { 4 / 3 } - x ^ { 5 } + 5f(x) =x4/3−x5+5

Use the graph of a power function and transformations to sketch the graph of the polynomial function. - (x) =3−(x+2) 4( x ) = 3 - ( x + 2 ) ^ { 4 }(x) =3−(x+2) 4

State whether the function is a polynomial function or not. If it is, give its degree. - f(x) =6−x36f ( x ) = \frac { 6 - x ^ { 3 } } { 6 }f(x) =66−x3​

Use the graph of a power function and transformations to sketch the graph of the polynomial function. -

Use the graph of a power function and transformations to sketch the graph of the polynomial function. - f(x) =(x+5) 4+3f ( x ) = ( x + 5 ) ^ { 4 } + 3f(x) =(x+5) 4+3

Solve the problem. -You have 80 feet of fencing to enclose a rectangular region. What is the maximum area?

State whether the function is a polynomial function or not. If it is, give its degree. - f(x) =1−15xf ( x ) = 1 - \frac { 1 } { 5 } xf(x) =1−51​x

State whether the function is a polynomial function or not. If it is, give its degree. - f(x) =3x+7x4f ( x ) = 3 x + 7 x ^ { 4 }f(x) =3x+7x4

State whether the function is a polynomial function or not. If it is, give its degree. - f(x) =x4−7x5f ( x ) = \frac { x ^ { 4 } - 7 } { x ^ { 5 } }f(x) =x5x4−7​

Use the graph of a power function and transformations to sketch the graph of the polynomial function. - f(x) =(x−4) 4f ( x ) = ( x - 4 ) ^ { 4 }f(x) =(x−4) 4

Use the graph of a power function and transformations to sketch the graph of the polynomial function. - f(x) =−12x4f ( x ) = - \frac { 1 } { 2 } x ^ { 4 }f(x) =−21​x4

Use the graph of a power function and transformations to sketch the graph of the polynomial function. -

Use the graph of a power function and transformations to sketch the graph of the polynomial function. -

Solve the problem. -You have 76 feet of fencing to enclose a rectangular plot that borders on a river. If you do not fence the side along the river, find the length and width of the plot that will maximize the area.

Use the graph of a power function and transformations to sketch the graph of the polynomial function. -

State whether the function is a polynomial function or not. If it is, give its degree. - f(x) =12x4−2x3+2f ( x ) = 12 x ^ { 4 } - 2 x ^ { 3 } + 2f(x) =12x4−2x3+2

State whether the function is a polynomial function or not. If it is, give its degree. -f(x) = 6

Use the graph of a power function and transformations to sketch the graph of the polynomial function. - f(x) =12(x+3) 4+2f ( x ) = \frac { 1 } { 2 } ( x + 3 ) ^ { 4 } + 2f(x) =21​(x+3) 4+2

Use the graph of a power function and transformations to sketch the graph of the polynomial function. - f(x) =−15x5f ( x ) = - \frac { 1 } { 5 } x ^ { 5 }f(x) =−51​x5

Use the graph of a power function and transformations to sketch the graph of the polynomial function. -

State whether the function is a polynomial function or not. If it is, give its degree. - $f ( x ) = x ^ { 4 / 3 } - x ^ { 5 } + 5$

Use the graph of a power function and transformations to sketch the graph of the polynomial function. - $( x ) = 3 - ( x + 2 ) ^ { 4 }$ $Use the graph of a power function and transformations to sketch the graph of the polynomial function. - ( x ) = 3 - ( x + 2 ) ^ { 4 } A) B) C) D)$

State whether the function is a polynomial function or not. If it is, give its degree. - $f ( x ) = \frac { 6 - x ^ { 3 } } { 6 }$

Use the graph of a power function and transformations to sketch the graph of the polynomial function. - $f ( x ) = ( x + 5 ) ^ { 4 } + 3$ $Use the graph of a power function and transformations to sketch the graph of the polynomial function. - f ( x ) = ( x + 5 ) ^ { 4 } + 3 A) B) C) D)$

State whether the function is a polynomial function or not. If it is, give its degree. - $f ( x ) = 1 - \frac { 1 } { 5 } x$

State whether the function is a polynomial function or not. If it is, give its degree. - $f ( x ) = 3 x + 7 x ^ { 4 }$

State whether the function is a polynomial function or not. If it is, give its degree. - $f ( x ) = \frac { x ^ { 4 } - 7 } { x ^ { 5 } }$

Use the graph of a power function and transformations to sketch the graph of the polynomial function. - $f ( x ) = ( x - 4 ) ^ { 4 }$ $Use the graph of a power function and transformations to sketch the graph of the polynomial function. - f ( x ) = ( x - 4 ) ^ { 4 } A) B) C) D)$

State whether the function is a polynomial function or not. If it is, give its degree. - $f ( x ) = 12 x ^ { 4 } - 2 x ^ { 3 } + 2$