Q: If $$f(x) = \frac{x^2$ - 1}{x - 1}$$, what is the lowest terms expression for $$f(x)$$ and its domain?

$$f(x) = x + 1$$, domain: $$x \neq 1$$

Question 1

Which of the following is the correct vertex form of a quadratic function?

Accepted Answer

$$f(x) = a(x - h)^2$ + k$$

Question 2

Given the quadratic function $$f(x) = 2x^2$ - 4x + 6$$, what is the axis of symmetry?

Accepted Answer

$$x = 2$$

Question 3

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

Accepted Answer

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

Question 4

Which of the following is NOT a polynomial function?

Accepted Answer

$$f(x) = 2x$$^{-1}$$ + 5$$

Question 5

What is the end behavior of $$f(x) = -3x^5$ + 2x^3$ - x as$$ $$x 	o \infty$$?

Accepted Answer

$$f(x) 	o -\infty$$

Question 6

For the polynomial $$f(x) = (x - 2)^2$(x + 1)$$, what is the multiplicity of the zero at $$x = 2$$ and does the graph touch or cross the $$x-$$axis at this point?

Accepted Answer

Multiplicity 2, graph touches the $$x-$$axis

Question 7

What is the maximum number of turning points for the polynomial $$f(x) = x^4$ - 2x^2$ + 1$$?

Accepted Answer

3

Question 8

Given the rational function $$f(x) = \frac{x^2$ - 9}{x^2$ - 4}$$, what are the vertical asymptotes?

Accepted Answer

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

Question 9

For the rational function $$f(x) = \frac{2x^2$ + 1}{x^2$ - 1}$$, what is the horizontal asymptote?

Accepted Answer

$$y = 2$$

Question 10

Which transformation will shift the graph of $$f(x) = x^2$ 3 units to the right and 2 units up?

Accepted Answer

$$f(x) = (x - 3)^2$ + 2$$

Question 11

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

Accepted Answer

$$x = 2$$

Question 12

Which of the following best describes the domain of the rational function $$f(x) = \frac{1}{x^2$ - 9}$$?

Accepted Answer

All real numbers except $$x = 3$$ and $$x = -3$$

Question 13

If $$f(x) = x^3$ - 6x^2$ + 11x - 6$$, what are the zeros of the function?

Accepted Answer

$$x = 1, 2, 3$$

Question 14

Which of the following graphs could represent a polynomial of degree 4 with a negative leading coefficient?

Accepted Answer

Both ends fall to $$-\infty$$

Question 15

Given $$f(x) = \frac{2x^2$ + 3x}{x^2$ - 1}$$, what is the $$y-$$intercept of the function?

Accepted Answer

$$y = 0$$

Question 16

For the polynomial $$f(x) = (x - 1)^3$(x + 2)$$, what is the behavior of the graph at $$x = 1$$?

Accepted Answer

The graph crosses the $$x-$$axis with a flattening effect

Question 17

Which of the following rational functions has a horizontal asymptote at $$y = 0$$?

Accepted Answer

$$f(x) = \frac{2x}{x^2$ + 1}$$

Question 18

If $$f(x) = \frac{x^2$ - 1}{x - 1}$$, what is the lowest terms expression for $$f(x)$$ and its domain?

Accepted Answer

$$f(x) = x + 1$$, domain: $$x 
eq 1$$

Question 19

A rational function $$f(x) = \frac{x^2$ + 2x + 1}{x^2$ - 1} is $$transformed by shifting 2 units left and 3 units up. What is the new function?

Accepted Answer

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

Precalculus Study Guide: Polynomial and Rational Functions (Ch. 3)

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