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

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

Question 1

Given the function $$D(x) = 150 - 20x$$ representing the distance in miles a train is from a station after $$x$$ hours, what is the value of $$D(5)$$ and what does it represent?

Accepted Answer

$$D(5) = 50$$, which means the train is 50 miles from the station after 5 hours.

Question 2

For the function $$D(x) = 150 - 20x$$, what is the slope of the graph, and what does it represent in this context?

Accepted Answer

The slope is $$-20$$, representing the train moving toward the station at 20 miles per hour.

Question 3

Which of the following is a reasonable domain for the function $$D(x) = 150 - 20x if$$ $$D(x)$$ represents the distance a train is from a station?

Accepted Answer

$$0 \leq x \leq 7.5$$

Question 4

Which of the following equations is NOT continuous for all real numbers?

Accepted Answer

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

Question 5

According to the Fundamental Theorem of Algebra, how many zeros (real or complex) does the polynomial $$P(x) = x^4$ - 4x^2$ - 5$$ have?

Accepted Answer

4 zeros

Question 6

What does the Conjugate Zeros Theorem state about the zeros of a polynomial with real coefficients?

Accepted Answer

If $$a + bi is a $$zero, then $$a - bi is $$also a zero.

Question 7

Fully factor $$x^4$$ - $$4x^2 - 5$ over the complex numbers.

Accepted Answer

$$(x^2$$ - $$5)(x^2 + 1) = (x$$ - \sqrt{5})(x + \sqrt{5})(x - i)(x + i)$$

Question 8

Given the graph of $$f(x) in $$image 3, what are the zeros of $$f$$?

Accepted Answer

$$x = -2, x = 0, x = 2$$

Question 9

For the function $$f(x) in $$image 3, on which interval is $$f(x)$$ increasing?

Accepted Answer

$$x \in (-2, 0)$$

Question 10

For the function $$f(x) in $$image 3, is the average rate of change from $$x = -4 to$$ $$x = 4$$ positive, negative, or zero?

Accepted Answer

Negative

Question 11

Which of the following is the correct sketch for $$y = x^3$?

Accepted Answer

A graph that passes through the origin, is increasing everywhere, and has point symmetry about the origin.

Question 12

Which function has a domain of all real numbers except $$x = 0$$?

Accepted Answer

$$f(x) = x$$^{-1}$$

Question 13

If $$f(x) = x$$^{1/2}$$, what is the domain of f$?

Accepted Answer

$$x \geq 0$$

Question 14

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

Accepted Answer

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

Question 15

Which of the following is the correct quotient and remainder when dividing $$x^3$$ - $$2x^2 + 5x - 3$ by x - 1$?

Accepted Answer

Quotient: $$x^2 - x + 4$, Remainder: 1$

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