Question 1

Which of the following is NOT a polynomial function?

Accepted Answer

$$f(x) = \dfrac{1}{x} + 2$$

Question 2

Given $$f(x) = -3x^4$ + 2x^2$ - x + 5$$, what is the degree and leading coefficient of the polynomial?

Accepted Answer

Degree: $$4$$, Leading Coefficient: $$-3$$

Question 3

Which of the following graphs could represent a polynomial function?

Accepted Answer

A graph that is smooth and continuous

Question 4

What is the end behavior of $$f(x) = -2x^5$ + x^3$ - 7 as$$ $$x 	o \infty$$?

Accepted Answer

$$f(x) 	o -\infty$$

Question 5

For the polynomial $$f(x) = (x-2)^2$(x+1)$$, what are the zeros and their multiplicities?

Accepted Answer

Zero at $$x=2 ($$multiplicity 2), $$x=-1 ($$multiplicity 1)

Question 6

If a polynomial has a zero at $$x=3$$ with multiplicity 3, what does the graph do at $$x=3$$?

Accepted Answer

Crosses the x-axis

Question 7

What is the maximum number of turning points for the polynomial $$f(x) = x^6$ - 2x^4$ + x$$?

Accepted Answer

$$5$$

Question 8

Which of the following best describes the end behavior of $$f(x) = 4x^8$ - x^2$ + 7$$?

Accepted Answer

Both ends rise

Question 9

Given $$f(x) = x^2$(x-1)^3(x+2$$)$$, how many distinct real zeros does f(x$$)$ have?

Accepted Answer

$$3$$

Question 10

A polynomial function has degree 7. What is the maximum number of turning points it can have?

Accepted Answer

$$6$$

Question 11

Which of the following is the standard form of the polynomial $$f(x) = x(x-2)(x+3)$$?

Accepted Answer

$$x^3$$ + $$x^2 - 6x$

Question 12

If $$f(x) = -x^4$ + 2x^2$ - 5$$, what is the end behavior as $$x 	o -\infty$$?

Accepted Answer

$$f(x) 	o -\infty$$

Question 13

Which of the following statements is TRUE about all polynomial functions?

Accepted Answer

Their graphs are always smooth and continuous

Question 14

Given $$f(x) = (x+1)^2$(x-3)^4$, what is the degree of the polynomial?

Accepted Answer

$$6$$

Question 15

Which of the following could be the graph of $$f(x) = x^3$ - 2x^2$ + x$$?

Accepted Answer

A graph with two turning points

Question 16

If $$f(x) = (x-1)^2$(x+2)$$, what does the graph do at $$x=1$$?

Accepted Answer

Touches the x-axis and turns around

Question 17

Which of the following is NOT a characteristic of polynomial functions?

Accepted Answer

They have holes in their graphs

Question 18

Given $$f(x) = -2(x+1)^3$(x-2)^2$$, what is the end behavior as $$x 	o \infty$?

Accepted Answer

$$f(x) 	o -\infty$$

Question 19

If $$f(x) = x^4$ - 2x^2$ + 1$$, how many real zeros does the function have?

Accepted Answer

$$2 ($$double roots at $$x=1$$ and $$x=-1)$$

Question 20

A real-world scenario: The height $$h (in $$meters) of a projectile at time $$t (in $$seconds) is modeled by $$h(t) = -5t^2$ + 20t + 1. Is $$this a polynomial function, and what is its degree?

Accepted Answer

Yes, degree 2

Understanding Polynomial Functions: Structure, Graphs, Zeros, and Turning Points

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