Q: Which of the following best describes the end behavior of the polynomial $$f(x) = -2x^5$ + 3x^2$ - x + 8$$?

As $$x \to \infty$$, $$f(x) \to -\infty$$; as $$x \to -\infty$$, $$f(x) \to \infty$$

Q: A polynomial function $$h(x)$$ has a degree of 6 and a positive leading coefficient. What is the end behavior of $$h(x)$$?

As $$x \to \infty$$, $$h(x) \to \infty$$; as $$x \to -\infty$$, $$h(x) \to \infty$$

Q: If a polynomial $$p(x)$$ has a degree of 3, which of the following could be its graph's end behavior?

As $$x \to \infty$$, $$p(x) \to \infty$$; as $$x \to -\infty$$, $$p(x) \to -\infty$$

Q: Which of the following statements is true about the graph of a polynomial of odd degree with a positive leading coefficient?

As $$x \to \infty$$, $$f(x) \to \infty$$; as $$x \to -\infty$$, $$f(x) \to -\infty$$

Question 1

Which of the following expressions is a polynomial?

Accepted Answer

$$x^3 - 4x + 7$

Question 2

What is the degree and leading coefficient of the polynomial $$5x^4$$ - $$3x^2 + 2x - 7$?

Accepted Answer

Degree: 4, Leading Coefficient: 5

Question 3

Which of the following best describes the end behavior of the polynomial $$f(x) = -2x^5$ + 3x^2$ - x + 8$$?

Accepted Answer

As $$x 	o \infty$$, $$f(x) 	o -\infty$$; as $$x 	o -\infty$$, $$f(x) 	o \infty$$

Question 4

Given the polynomial $$g(x) = 4x^3$ - x^2$ + 6$$, what is the value of $$g(-2)$$?

Accepted Answer

$$-38$$

Question 5

Which of the following is NOT a polynomial function?

Accepted Answer

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

Question 6

A polynomial function $$h(x)$$ has a degree of 6 and a positive leading coefficient. What is the end behavior of $$h(x)$$?

Accepted Answer

As $$x 	o \infty$$, $$h(x) 	o \infty$$; as $$x 	o -\infty$$, $$h(x) 	o \infty$$

Question 7

If a polynomial $$p(x)$$ has a degree of 3, which of the following could be its graph's end behavior?

Accepted Answer

As $$x 	o \infty$$, $$p(x) 	o \infty$$; as $$x 	o -\infty$$, $$p(x) 	o -\infty$$

Question 8

Which of the following real-world scenarios can be modeled by a polynomial function?

Accepted Answer

The area of a rectangular garden as a function of its length when the width is fixed

Question 9

Given the polynomial $$f(x) = 2x^4$ - 5x^3$ + x - 9$$, what is the leading term?

Accepted Answer

$$2x^4$$

Question 10

A company models its profit $$P(x) in $$thousands of dollars as $$P(x) = -3x^2$ + 12x - 5$$, where $$x is $$the number of units sold in hundreds. What is the degree of this polynomial, and what does the negative leading coefficient indicate about the profit as $$x$$ increases?

Accepted Answer

Degree: 2; Profit will eventually decrease as $$x$$ increases

Question 11

Which of the following is the correct standard form of the polynomial $$3x - x^4$ + 2x^2$?

Accepted Answer

$$-x^4$$ + $$2x^2 + 3x$

Question 12

If $$f(x) = x^2$ - 4x + 3$$, what is $$f(5)$$?

Accepted Answer

$$8$$

Question 13

Which of the following statements is true about the graph of a polynomial of odd degree with a positive leading coefficient?

Accepted Answer

As $$x 	o \infty$$, $$f(x) 	o \infty$$; as $$x 	o -\infty$$, $$f(x) 	o -\infty$$

Question 14

A polynomial $$p(x) is $$given by $$p(x) = 7x^2$ - 4x + 1. $$What is the value of the leading coefficient?

Accepted Answer

$$7$$

Question 15

Which of the following is the degree of the polynomial $$q(x) = 2x^5$ - 3x^3$ + 4x^2$ - x + 6$$?

Accepted Answer

$$5$$

Question 16

If the end behavior of a polynomial $$f(x) is $$such that as $$x 	o \infty$$, $$f(x) 	o -\infty$$ and as $$x 	o -\infty$$, $$f(x) 	o -\infty$$, what can you conclude about the degree and leading coefficient?

Accepted Answer

Even degree, negative leading coefficient

Polynomials: Degree, Leading Coefficient, Graphs, and End Behavior

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