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

Question 1

Which of the following expressions is a polynomial?

Accepted Answer

$$f(x) = 4x^2$ - 7x + 9$$

Question 2

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

Accepted Answer

Degree: 4, Leading coefficient: 2

Question 3

Which of the following is the correct standard form of the equation of a circle with center $$(3, -2)$$ and radius $$5$$?

Accepted Answer

$$(x - 3)^2$ + (y + 2)^2$ = 25$$

Question 4

Solve the inequality $$2x - 5 \u003c 7.$$

Accepted Answer

$$x \u003c 4$$

Question 5

If $$f(x) = x^3$ - 4x^2$ + x + 6 is $$divided by $$x - 2$$, what is the remainder?

Accepted Answer

$$2$$

Question 6

Which of the following is a rational function?

Accepted Answer

$$f(x) = \dfrac{3x + 2}{x - 1}$$

Question 7

A circle has the equation $$x^2$$ + $$y^2 - 6x + 8y = 0$. What are the center and radius of the circle?

Accepted Answer

Center: $$(3, -4)$$, Radius: $$5$$

Question 8

Which of the following statements about the Fundamental Theorem of Algebra is correct?

Accepted Answer

A polynomial of degree $$n$$ has exactly $$n$$ complex zeros, counting multiplicities.

Question 9

Solve the radical equation: $$\sqrt{x + 5} = x - 1.$$

Accepted Answer

$$x = 3$$

Question 10

Which of the following describes inverse variation?

Accepted Answer

$$y = \dfrac{k}{x}$$

Question 11

Given the rational function $$f(x) = \dfrac{2x^2$ - 3x + 1}{x^2$ - 4}$$, what are the vertical asymptotes?

Accepted Answer

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

Question 12

If $$y$$ varies directly as $$x$$ and $$y = 10$$ when $$x = 2$$, what is the value of $$y$$ when $$x = 5$$?

Accepted Answer

$$y = 15$$

Question 13

Which of the following is NOT a possible rational zero of $$f(x) = 6x^3$ - 5x^2$ + 2x - 1$$ according to the Rational Zero Theorem?

Accepted Answer

$$\dfrac{2}{3}$$

Question 14

Solve the rational equation: $$\dfrac{x}{x-2} = 3.$$

Accepted Answer

$$x = 6$$

Question 15

Which of the following best describes the end behavior of $$f(x) = -2x^5$ + 3x^2$ - 7$$?

Accepted Answer

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

Question 16

Which of the following is the correct equation of a circle with diameter endpoints at $$(1, 2)$$ and $$(5, 6)$$?

Accepted Answer

$$(x - 3)^2$ + (y - 4)^2$ = 8$$

Question 17

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

Accepted Answer

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

Question 18

Which of the following is the solution set for the inequality $$x^2 - 9$$ \u003c 0$$?

Accepted Answer

$$-3 \u003c x \u003c 3$$

Question 19

A rational function has a horizontal asymptote at $$y = 0. $$Which of the following could be its equation?

Accepted Answer

$$f(x) = \dfrac{2x^2$ + 1}{x^3$ - 4}$$

College Algebra: Study Guide for Polynomial, Rational, Radical Functions, and Circles

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