Q: Which statement about the end behavior of the polynomial $$f(x) = -2x^5$ + 3x^2$ - x + 7 is $$correct?

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

Question 1

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

Accepted Answer

The variable is raised to a negative integer power.

Question 2

Given the polynomial $$f(x) = x^3$ - 4x^2$ + 5x - 2$$, which of the following is a possible rational zero according to the Rational Zeros Theorem?

Accepted Answer

$$2$$

Question 3

A polynomial function $$f(x)$$ has real zeros at $$x = -2, 1, 3$$ and $$f(x) is of $$degree 4. Which of the following could be the factored form of $$f(x)$$?

Accepted Answer

$$f(x) = (x+2)^2$(x-1)(x-3)$$

Question 4

Which statement about the end behavior of the polynomial $$f(x) = -2x^5$ + 3x^2$ - x + 7 is $$correct?

Accepted Answer

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

Question 5

If $$f(x) = x^4$ - 5x^2$ + 4$$, what is the maximum number of turning points the graph of $$f(x)$$ can have?

Accepted Answer

$$3$$

Question 6

A rational function $$R(x) = \frac{2x^2$ - 3x + 1}{x^2$ - 4}$$ has which of the following vertical asymptotes?

Accepted Answer

$$x = 2$$ and $$x = -2$$

Question 7

Which of the following describes the domain of the function $$h(x) = \frac{x^2$}{x^2$ - 9}$$?

Accepted Answer

$$(-\infty, -3) \cup (-3, 3) \cup (3, \infty)$$

Question 8

Given $$f(x) = x^3$ - 2x^2$ + x - 2$$, use the Remainder Theorem to find the remainder when $$f(x) is $$divided by $$x - 2.$$

Accepted Answer

$$0$$

Question 9

Which of the following is the correct interval notation for the solution to the inequality $$x^2 - 4$$ \u003c 0$$?

Accepted Answer

$$(-2, 2)$$

Question 10

A rational function $$f(x) = \frac{3x^2$ + 2x - 1}{x - 1}$$ has which of the following oblique asymptotes?

Accepted Answer

Question 11

If $$f(x) = x^3$ - 6x^2$ + 11x - 6$$, which of the following is a factor of $$f(x)$$?

Accepted Answer

$$x - 1$$

Question 12

Which of the following is the correct application of the Intermediate Value Theorem?

Accepted Answer

If $$f(a)$$ and $$f(b)$$ have opposite signs, then $$f(x)$$ has a zero between $$a$$ and $$b.$$

Question 13

Given $$f(x) = x^2$ - 4x + 3$$, which of the following is the correct set of $$x-$$intercepts?

Accepted Answer

$$x = 1$$ and $$x = 3$$

Question 14

Which of the following is the correct domain for the function $$g(x) = \sqrt{x - 2}$$?

Accepted Answer

$$[2, \infty)$$

Question 15

If $$f(x) = x^2$ + 2x + 1$$, what is the vertex of the parabola?

Accepted Answer

$$(-1, 0)$$

Question 16

Which of the following is the correct range for the function $$f(x) = \frac{1}{x}$$?

Accepted Answer

$$(-\infty, 0) \cup (0, \infty)$$

Question 17

Which of the following is the correct solution to the inequality $$x^2 + 5x$$ \u003c 0$$?

Accepted Answer

$$(-5, 0)$$

Question 18

Given $$f(x) = x^2$ - 6x + 9$$, which of the following describes the graph of $$f(x)$$?

Accepted Answer

A parabola opening upwards with vertex at $$(3, 0)$$

Question 19

Which of the following is the correct set of real zeros for $$f(x) = x^3$ - 6x^2$ + 11x - 6$$?

Accepted Answer

$$1, 2, 3$$

Question 20

Which of the following is the correct interval notation for the solution to the inequality $$x^2 - 9$$ \geq 0$$?

Accepted Answer

$$(-\infty, -3] \cup [3, \infty)$$

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