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 $$f(x) = 3x^2$ - 6x + 2$$, what is the $$x-$$coordinate of its vertex?

Accepted Answer

$$x = 1$$

Question 3

A rational function $$f(x) = \frac{x^2$ - 9}{x^2$ - 4}$$ has which of the following features?

Accepted Answer

Vertical asymptotes at $$x = 2$$ and $$x = -2$$

Question 4

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

Accepted Answer

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

Question 5

Which of the following is NOT a root of the polynomial $$f(x) = x^2$ + 4$$?

Accepted Answer

$$x = 2$$

Question 6

A rational function $$f(x) = \frac{(x-1)(x+2)}{(x-1)(x-3)}$$ has a hole at which $$x$$ value?

Accepted Answer

$$x = 1$$

Question 7

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

Accepted Answer

$$y = 2$$

Question 8

Which of the following statements about the domain of $$f(x) = \frac{1}{x} + \frac{1}{x-3} is $$correct?

Accepted Answer

The domain excludes $$x = 0$$ and $$x = 3$$

Question 9

If $$f(x) = x^2$ - 6x + 8$$, what is the minimum value of $$f(x)$$?

Accepted Answer

Question 10

Which theorem helps you determine possible rational roots of a polynomial with integer coefficients?

Accepted Answer

Rational Root Theorem

Question 11

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

Accepted Answer

$$y = 1$$

Question 12

Which of the following is true about the roots of $$f(x) = x^2$ + 9$$?

Accepted Answer

Both roots are imaginary

Question 13

Synthetic division is most useful for which of the following tasks?

Accepted Answer

Dividing a polynomial by a linear factor

Question 14

If $$f(x) = \frac{x^2$ - 4}{x^2$ - 4x + 4}$$, what is the domain of $$f(x)$$?

Accepted Answer

All real numbers except $$x = 2$$

Question 15

Descartes' Rule of Signs is used to:

Accepted Answer

Predict the number of positive and negative real roots of a polynomial

Question 16

If $$f(x) = x^2$ - 5x + 6$$, which values of $$x$$ make $$f(x) = 0$$?

Accepted Answer

$$x = 2$$ and $$x = 3$$

Question 17

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

$$24.4$$ meters

Question 18

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

Accepted Answer

$$x = 2$$ and $$x = -1$$

Question 19

If a polynomial has a root at $$x = 3 + 2i$$, what other root must it have?

Accepted Answer

$$x = 3 - 2i$$

Question 20

Which of the following best describes the range of the parabola $$f(x) = -x^2$ + 4x - 1$$?

Accepted Answer

All real numbers less than or equal to $$7$$

Precalculus Study Notes: Functions, Parabolas, and Rational Functions

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