Q: Which of the following best describes the end behavior of the function $$f(x) = x^3$ - 8x + 1$$?

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

Question 1

Which of the following is the correct standard form of the equation $$x^3 - 8x + 1 = 0$?

Accepted Answer

$$x^3 - 8x + 1 = 0$

Question 2

What is the degree of the polynomial $$x^3 - 8x + 1$?

Accepted Answer

3

Question 3

Which of the following is a possible rational root of $$x^3 - 8x + 1 = 0$ according to the Rational Root Theorem?

Accepted Answer

$$1$$

Question 4

If you use a graphing utility to approximate the real solution of $$x^3 - 8x + 1 = 0$, which of the following is closest to the real root?

Accepted Answer

$$x \approx 2.12$$

Question 5

Rewrite the equation $$2 - \frac{4}{3}x^2$ = x^3$ - \frac{5}{2}x in $$standard form.

Accepted Answer

$$x^3$$ + \frac{4}{3}$$x^2$$ - \frac{5}{2}x - 2 = 0$$

Question 6

Which of the following best describes the end behavior of the function $$f(x) = x^3$ - 8x + 1$$?

Accepted Answer

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

Question 7

Which of the following is the leading coefficient of the polynomial $$x^3 - 8x + 1$?

Accepted Answer

1

Question 8

If $$x = 1 is $$substituted into $$x^3 - 8x + 1$, what is the result?

Accepted Answer

$$-6$$

Question 9

Which of the following describes the number of real roots for the equation $$x^3 - 8x + 1 = 0$?

Accepted Answer

There is exactly one real root.

Question 10

Suppose you are modeling the height (in meters) of a projectile with the equation $$h(t) = t^3$ - 8t + 1. $$What does the solution to $$t^3 - 8t + 1 = 0$ represent in this context?

Accepted Answer

The time when the projectile is at ground level.

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