Question 1

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
-The end behavior of the graph of $f ( x ) = - 8 x ^ { 3 }$ is (up/down) to the left and (up/down) to the right.

Accepted Answer

The answer of Write the word or phrase that best...

Question 2

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
-If c is a real zero of a polynomial function and the multiplicity is 6, does the graph of the function
cross the x-axis or touch the x-axis (without crossing) at (c, 0)?

Accepted Answer

The answer of Write the word or phrase that best...

Question 3

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
-The values of x in the domain of a polynomial function f for which $f ( x ) = 0$ are called the
of the function.

Accepted Answer

The answer of Write the word or phrase that best...

Question 4

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
-The function defined by $f ( x ) = \frac { 1 } { x }$ is continuous.

Accepted Answer

The function $f(x) = \frac{1}{x}$ is not continuous at $x = 0$ because it is undefined at that point, causing a discontinuity.

Question 5

Choose the one alternative that best completes the statement or answers the question.
Determine the end behavior of the graph of the function.
-$$f ( x ) = 8 x ^ { 6 } + 3 x ^ { 5 } + 3 x ^ { 4 } + 7$$

Accepted Answer

The leading term of the polynomial function $f(x) = 8x^6 + 3x^5 + 3x^4 + 7$ is $8x^6$. Since the coefficient of the leading term (8) is positive and the degree of the polynomial (6) is even, the end behavior of the graph is up on both the left and right sides.

Question 6

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
-The end behavior of the graph of $f ( x ) = - 6 x ^ { 2 }$ is (up/down) to the left and (up/down) to the right.

Accepted Answer

The answer of Write the word or phrase that best...

Question 7

Find the zeros of the function and state the multiplicities.
-$$f ( x ) = 2 x ^ { 5 } + 9 x ^ { 4 } + 7 x ^ { 3 }$$

Accepted Answer

First, factor out the greatest common factor, which is $x^3$, giving $x^3(2x^2 + 9x + 7)$. The zeros are found by setting $x^3 = 0$ and $2x^2 + 9x + 7 = 0$. The first equation gives a zero at $x = 0$ with multiplicity 3. Solving the quadratic equation $2x^2 + 9x + 7 = 0$ using the quadratic formula or factoring (if possible) would give the other zeros, which are not $1$ or $\frac{7}{2}$ as in choices B and C, and multiplicities are always whole numbers, ruling out choice A.

Question 8

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
-Suppose that f is a polynomial function and that a < b. If f(a) and f(b) have opposite signs, then what
conclusion can be drawn from the intermediate value theorem?

Accepted Answer

The answer of Write the word or phrase that best...

Question 9

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
-Given the function defined by $h ( x ) = \frac { 1 } { 2 } x ^ { 5 } ( x + 0.6 ) ^ { 3 }$ , the value 0 is a zero with multiplicity ,
and the value -0.6 is a zero with multiplicity .

Accepted Answer

The answer of Write the word or phrase that best...

Question 10

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
-If the graph of a polynomial function has 3 turning points, what is the minimum degree of the
function?

Accepted Answer

The answer of Write the word or phrase that best...

Question 11

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
-What is the maximum number of turning points of the graph of $f ( x ) = - 3 x ^ { 6 } - 4 x ^ { 5 } - 5 x ^ { 4 } + 2 x ^ { 2 } + 6$

Accepted Answer

The answer of Write the word or phrase that best...

Question 12

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
-What is the leading term of $f ( x ) = - \frac { 1 } { 3 } ( x - 3 ) ^ { 4 } ( 3 x + 5 ) ^ { 2 }$ ?

Accepted Answer

The answer of Write the word or phrase that best...

Question 13

Choose the one alternative that best completes the statement or answers the question.
Determine the end behavior of the graph of the function.
-$$f ( x ) = 8 x ^ { 3 } ( 4 - x ) ( 7 x - 6 ) ^ { 4 }$$

Accepted Answer

The leading term is $8x^3(4-x)(7x-6)^4$. Since the leading coefficient is positive and the degree of the polynomial is odd, the graph falls to the left and falls to the right.

Question 14

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
-What is the leading term of $f ( x ) = - 0.6 x ^ { 2 } ( 10 x + 1 ) ^ { 3 } ( x - 1 ) ^ { 4 }$ ?

Accepted Answer

The answer of Write the word or phrase that best...

Question 15

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
-Given the function defined by $g ( x ) = - 3 ( x - 1 ) ^ { 3 } ( x + 5 ) ^ { 4 }$ , the value 1 is a zero with multiplicity
, and the value -5 is a zero with multiplicity .

Accepted Answer

The answer of Write the word or phrase that best...

Question 16

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
-If c is a real zero of a polynomial function and the multiplicity is 3, does the graph of the function
cross the x-axis or touch the x-axis (without crossing) at (c, 0)?

Accepted Answer

The answer of Write the word or phrase that best...

Question 17

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
-An even function is symmetric with respect to the axis.

Accepted Answer

The answer of Write the word or phrase that best...

Question 18

Choose the one alternative that best completes the statement or answers the question.
Determine the end behavior of the graph of the function.
-$$4 ( x + 2 ) ( 8 x + 7 ) ^ { 3 } ( x + 2 ) ^ { 5 }$$

Accepted Answer

The function's leading term, when expanded, will have a positive coefficient and an even degree, leading to both ends of the graph pointing in the same direction, upwards, as $x$ approaches both $-\infty$ and $\infty$.

Question 19

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
-An odd function is symmetric with respect to the .

Accepted Answer

The answer of Write the word or phrase that best...

Question 20

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
-If the leading term of a polynomial function is $a x ^ { n }$ where a is negative and n is odd, determine the
end behavior.

Accepted Answer

The answer of Write the word or phrase that best...

Quiz 3: Polynomial and Rational Functions

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -The end behavior of the graph of $f ( x ) = - 8 x ^ { 3 }$ is (up/down) to the left and (up/down) to the right.

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -If c is a real zero of a polynomial function and the multiplicity is 6, does the graph of the function cross the x-axis or touch the x-axis (without crossing) at (c, 0)?

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -The values of x in the domain of a polynomial function f for which $f ( x ) = 0$ are called the of the function.

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -The function defined by $f ( x ) = \frac { 1 } { x }$ is continuous.

Choose the one alternative that best completes the statement or answers the question. Determine the end behavior of the graph of the function. - $f ( x ) = 8 x ^ { 6 } + 3 x ^ { 5 } + 3 x ^ { 4 } + 7$

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -The end behavior of the graph of $f ( x ) = - 6 x ^ { 2 }$ is (up/down) to the left and (up/down) to the right.

Find the zeros of the function and state the multiplicities. - $f ( x ) = 2 x ^ { 5 } + 9 x ^ { 4 } + 7 x ^ { 3 }$

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -Suppose that f is a polynomial function and that a < b. If f(a) and f(b) have opposite signs, then what conclusion can be drawn from the intermediate value theorem?

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -If the graph of a polynomial function has 3 turning points, what is the minimum degree of the function?

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -What is the maximum number of turning points of the graph of $f ( x ) = - 3 x ^ { 6 } - 4 x ^ { 5 } - 5 x ^ { 4 } + 2 x ^ { 2 } + 6$

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -What is the leading term of $f ( x ) = - \frac { 1 } { 3 } ( x - 3 ) ^ { 4 } ( 3 x + 5 ) ^ { 2 }$ ?

Choose the one alternative that best completes the statement or answers the question. Determine the end behavior of the graph of the function. - $f ( x ) = 8 x ^ { 3 } ( 4 - x ) ( 7 x - 6 ) ^ { 4 }$

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -What is the leading term of $f ( x ) = - 0.6 x ^ { 2 } ( 10 x + 1 ) ^ { 3 } ( x - 1 ) ^ { 4 }$ ?

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -Given the function defined by $g ( x ) = - 3 ( x - 1 ) ^ { 3 } ( x + 5 ) ^ { 4 }$ , the value 1 is a zero with multiplicity , and the value -5 is a zero with multiplicity .

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -If c is a real zero of a polynomial function and the multiplicity is 3, does the graph of the function cross the x-axis or touch the x-axis (without crossing) at (c, 0)?

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -An even function is symmetric with respect to the axis.

Choose the one alternative that best completes the statement or answers the question. Determine the end behavior of the graph of the function. - $4 ( x + 2 ) ( 8 x + 7 ) ^ { 3 } ( x + 2 ) ^ { 5 }$

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -An odd function is symmetric with respect to the .

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -If the leading term of a polynomial function is $a x ^ { n }$ where a is negative and n is odd, determine the end behavior.

Quiz 3: Polynomial and Rational Functions

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -The end behavior of the graph of f(x)=−8x3f ( x ) = - 8 x ^ { 3 }f(x)=−8x3 is (up/down) to the left and (up/down) to the right.

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -If c is a real zero of a polynomial function and the multiplicity is 6, does the graph of the function cross the x-axis or touch the x-axis (without crossing) at (c, 0)?

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -The values of x in the domain of a polynomial function f for which f(x)=0f ( x ) = 0f(x)=0 are called the of the function.

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -The function defined by f(x)=1xf ( x ) = \frac { 1 } { x }f(x)=x1​ is continuous.

Choose the one alternative that best completes the statement or answers the question. Determine the end behavior of the graph of the function. - f(x) =8x6+3x5+3x4+7f ( x ) = 8 x ^ { 6 } + 3 x ^ { 5 } + 3 x ^ { 4 } + 7f(x) =8x6+3x5+3x4+7

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -The end behavior of the graph of f(x)=−6x2f ( x ) = - 6 x ^ { 2 }f(x)=−6x2 is (up/down) to the left and (up/down) to the right.

Find the zeros of the function and state the multiplicities. - f(x) =2x5+9x4+7x3f ( x ) = 2 x ^ { 5 } + 9 x ^ { 4 } + 7 x ^ { 3 }f(x) =2x5+9x4+7x3

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -Suppose that f is a polynomial function and that a < b. If f(a) and f(b) have opposite signs, then what conclusion can be drawn from the intermediate value theorem?

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -If the graph of a polynomial function has 3 turning points, what is the minimum degree of the function?

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -What is the leading term of f(x)=−13(x−3)4(3x+5)2f ( x ) = - \frac { 1 } { 3 } ( x - 3 ) ^ { 4 } ( 3 x + 5 ) ^ { 2 }f(x)=−31​(x−3)4(3x+5)2 ?

Choose the one alternative that best completes the statement or answers the question. Determine the end behavior of the graph of the function. - f(x) =8x3(4−x) (7x−6) 4f ( x ) = 8 x ^ { 3 } ( 4 - x ) ( 7 x - 6 ) ^ { 4 }f(x) =8x3(4−x) (7x−6) 4

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -What is the leading term of f(x)=−0.6x2(10x+1)3(x−1)4f ( x ) = - 0.6 x ^ { 2 } ( 10 x + 1 ) ^ { 3 } ( x - 1 ) ^ { 4 }f(x)=−0.6x2(10x+1)3(x−1)4 ?

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -If c is a real zero of a polynomial function and the multiplicity is 3, does the graph of the function cross the x-axis or touch the x-axis (without crossing) at (c, 0)?

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -An even function is symmetric with respect to the axis.

Choose the one alternative that best completes the statement or answers the question. Determine the end behavior of the graph of the function. - 4(x+2) (8x+7) 3(x+2) 54 ( x + 2 ) ( 8 x + 7 ) ^ { 3 } ( x + 2 ) ^ { 5 }4(x+2) (8x+7) 3(x+2) 5

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -An odd function is symmetric with respect to the .

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -If the leading term of a polynomial function is axna x ^ { n }axn where a is negative and n is odd, determine the end behavior.

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -The end behavior of the graph of $f ( x ) = - 8 x ^ { 3 }$ is (up/down) to the left and (up/down) to the right.

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -The values of x in the domain of a polynomial function f for which $f ( x ) = 0$ are called the of the function.

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -The function defined by $f ( x ) = \frac { 1 } { x }$ is continuous.

Choose the one alternative that best completes the statement or answers the question. Determine the end behavior of the graph of the function. - $f ( x ) = 8 x ^ { 6 } + 3 x ^ { 5 } + 3 x ^ { 4 } + 7$

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -The end behavior of the graph of $f ( x ) = - 6 x ^ { 2 }$ is (up/down) to the left and (up/down) to the right.

Find the zeros of the function and state the multiplicities. - $f ( x ) = 2 x ^ { 5 } + 9 x ^ { 4 } + 7 x ^ { 3 }$

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -What is the leading term of $f ( x ) = - \frac { 1 } { 3 } ( x - 3 ) ^ { 4 } ( 3 x + 5 ) ^ { 2 }$ ?

Choose the one alternative that best completes the statement or answers the question. Determine the end behavior of the graph of the function. - $f ( x ) = 8 x ^ { 3 } ( 4 - x ) ( 7 x - 6 ) ^ { 4 }$

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -What is the leading term of $f ( x ) = - 0.6 x ^ { 2 } ( 10 x + 1 ) ^ { 3 } ( x - 1 ) ^ { 4 }$ ?

Choose the one alternative that best completes the statement or answers the question. Determine the end behavior of the graph of the function. - $4 ( x + 2 ) ( 8 x + 7 ) ^ { 3 } ( x + 2 ) ^ { 5 }$

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -If the leading term of a polynomial function is $a x ^ { n }$ where a is negative and n is odd, determine the end behavior.