Question 1

Which of the following best describes the domain of the function $$f(x) = \frac{1}{x-2}$$?

Accepted Answer

All real numbers except $$x = 2$$

Question 2

Given the quadratic function $$f(x) = 2x^2$ - 4x + 1$$, what is the $$x-$$coordinate of its vertex?

Accepted Answer

$$x = 1$$

Question 3

If $$f(x) = x^2$ - 6x + 8$$, what are the $$x-$$intercepts of the parabola?

Accepted Answer

$$x = 2$$ and $$x = 4$$

Question 4

Which of the following is NOT a possible rational root of $$f(x) = 3x^3$ - 5x^2$ + 2x - 4$$ according to the Rational Root Theorem?

Accepted Answer

$$\frac{5}{3}$$

Question 5

A rational function $$f(x) = \frac{x^2$ - 9}{x^2$ - 4x + 3}$$ has a hole at which $$x$$ value?

Accepted Answer

$$x = 3$$

Question 6

What is the horizontal asymptote of $$f(x) = \frac{2x^2$ + 5}{x^2$ - 3x + 1}$$?

Accepted Answer

$$y = 2$$

Question 7

If $$f(x) = \frac{x+1}{x^2$-4}$$, which values must be excluded from the domain?

Accepted Answer

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

Question 8

Which statement about imaginary roots of polynomials is correct?

Accepted Answer

If $$a i is a $$root, then $$-a i is $$also a root.

Question 9

A parabola opens upward and has vertex at $$(2, -3). $$Which of the following could be its equation?

Accepted Answer

$$y = (x-2)^2$ - 3$$

Question 10

Which of the following best describes the range of $$f(x) = x^2$ - 4$$?

Accepted Answer

$$y \geq -4$$

Question 11

If $$f(x) = \frac{5 + x^2$ + \frac{1}{x} + \frac{1}{x-3}}{x}$$, which values of $$x$$ are NOT in the domain?

Accepted Answer

$$x = 0$$ and $$x = 3$$

Question 12

Which of the following is the result of expanding $$(x-2)(x+3)$$?

Accepted Answer

$$x^2 + x - 6$

Question 13

Descartes' Rule of Signs helps determine:

Accepted Answer

The possible number of positive and negative real roots of a polynomial

Question 14

Which of the following is true about synthetic division?

Accepted Answer

It is a shortcut for dividing polynomials by linear factors

Question 15

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

Accepted Answer

$$y = 1$$

Question 16

A rational function $$f(x) = \frac{x^2$ - 4}{x^2$ - 1}$$ has vertical asymptotes at:

Accepted Answer

$$x = 1$$ and $$x = -1$$

Question 17

Which of the following statements is correct regarding the roots and zeros of polynomials?

Accepted Answer

A root of a polynomial is a value that makes the function zero

Question 18

Given $$f(x) = \frac{x^2$ - 1}{x^2$ - 4}$$, what is the simplified form after factoring and cancelling common factors?

Accepted Answer

$$\frac{(x+1)(x-1)}{(x-2)(x+2)}$$

Question 19

A real-world scenario: The height $$h (in $$meters) of a projectile launched upward is given by $$h(t) = -4.9t^2$ + 20t + 2. $$What is the maximum height reached by the projectile?

Accepted Answer

$$22.04$$ meters

Precalculus Study Notes: Functions, Parabolas, and Rational Functions

Study Guide - Practice Questions

Study Guide - Flashcards