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

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 definition of a polynomial function?

Accepted Answer

A function of the form $$f(x) = a_nx^n + a$$_{n-1}$$x^{n-1}$$ + \ldots + a_1x + $$a_0$$, where $$a_n 
eq 0$$ and $$n$ is a non-negative integer.

Question 2

Given $$f(x) = 2x^3$ - 5x^2$ + 4x - 7$$, what is the degree of the polynomial?

Accepted Answer

3

Question 3

Which of the following is NOT a polynomial function?

Accepted Answer

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

Question 4

If $$f(x) = x^4$ - 2x^2$ + 1$$, what is the leading coefficient?

Accepted Answer

1

Question 5

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

Accepted Answer

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

Question 6

Which of the following is a possible rational root of $$f(x) = 2x^3$ - 3x^2$ + 4x - 6$$ according to the Rational Root Theorem?

Accepted Answer

$$\pm\frac{3}{2}$$

Question 7

If $$f(x) = x^2$ - 4x + 3$$, what are the zeros of the function?

Accepted Answer

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

Question 8

A chemical reaction rate is modeled by $$R(t) = 5t^2$ - 20t + 15. At $$what time $$t$$ does the reaction rate reach zero?

Accepted Answer

$$t = 1$$ and $$t = 3$$

Question 9

Which of the following is the correct factorization of $$f(x) = x^2$ - 9$$?

Accepted Answer

$$(x - 3)(x + 3)$$

Question 10

A population of bacteria is modeled by $$P(t) = t^3$ - 6t^2$ + 11t - 6. $$What is the initial population at $$t = 0$$?

Accepted Answer

6

Question 11

Which of the following is the remainder when $$f(x) = 2x^3$ + 5x^2$ - x + 4 is $$divided by $$x - 2$$?

Accepted Answer

38

Question 12

If $$f(x) = x^3$ - 2x^2$ + x - 2$$, which value of $$x is a $$root of the function?

Accepted Answer

$$x = 2$$

Question 13

Which of the following describes the graph of $$f(x) = x^2$?

Accepted Answer

A parabola opening upward with vertex at $$(0, 0)$$

Question 14

A company's profit is modeled by $$P(x) = -2x^2$ + 8x - 6$$, where $$x is $$the number of units sold. What is the maximum profit?

Accepted Answer

$$P(2) = 2$$

Question 15

Which of the following is the correct description of the zeros of $$f(x) = x^2$ + 4$$?

Accepted Answer

No real zeros

Question 16

If $$f(x) = x^3$ - 6x^2$ + 11x - 6$$, which of the following is NOT a root of the function?

Accepted Answer

$$x = 4$$

Question 17

Which of the following is the correct description of the multiplicity of the root $$x = 2$$ for $$f(x) = (x - 2)^3$(x + 1)$$?

Accepted Answer

Multiplicity 3

Question 18

A projectile's height is modeled by $$h(t) = -16t^2$ + 64t + 80. $$What is the maximum height reached by the projectile?

Accepted Answer

208

Question 19

Which of the following is the correct description of the end behavior of $$f(x) = 4x^4$ - x^2$ + 7$$?

Accepted Answer

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

Question 20

If $$f(x) = x^2$ - 2x + 1$$, which of the following is the correct factorization?

Accepted Answer

$$(x - 1)^2$

Exponential and Logarithmic Equations: Precalculus Study Notes

Study Guide - Practice Questions