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

Given the quadratic function $$f(x) = -3x^2$ - 9x - 6$$, what is the axis of symmetry?

Accepted Answer

$$x = -1.5$$

Question 2

For the quadratic function $$f(x) = \frac{1}{2}x^2$ + x - 4$$, what is the vertex?

Accepted Answer

$$(x, y) = (-1, -4.5)$$

Question 3

Which of the following describes the end behavior of $$f(x) = -3x^4$ + 6x^3$ - 3x^2$ + 2x - 8$$?

Accepted Answer

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

Question 4

Given $$g(x) = (x+7)(x+1)(x-5)^2$(x-8)$$, what is the multiplicity of the zero at $$x = -5$$?

Accepted Answer

2

Question 5

For the rational function $$f(x) = \frac{x^2$+4x+3}{x+1}$$, what is the vertical asymptote?

Accepted Answer

$$x = -1$$

Question 6

Using Descartes' Rule of Signs, how many possible positive real roots does $$f(x) = x^5$ + 3x^4$ - 5x^3$ + 2x^2$ - 4x - 4$$ have?

Accepted Answer

3 or 1

Question 7

Which transformation is applied to the parent function $$f(x) = x^2$ to obtain g(x$$) = $$-3(x-1)^2 + 7$?

Accepted Answer

Vertical stretch by 3, reflection over $$x-$$axis, right 1 unit, up 7 units

Question 8

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

Accepted Answer

Degree: 4, Leading coefficient: 2

Question 9

Given $$f(x) = \frac{x^2$-4}{x-2}$$, what is the $$y-$$intercept?

Accepted Answer

$$(0, -2)$$

Question 10

If $$f(x) = x^3$ - 6x^2$ + 5x - 12$$ and $$4 is a $$zero, what are all the zeros?

Accepted Answer

$$4, 3, -1$$

Question 11

For the rational function $$f(x) = \frac{x^2$+4x+3}{x+1}$$, does the graph intersect the horizontal asymptote?

Accepted Answer

No, because the degrees are not equal

Question 12

What is the end behavior of $$f(x) = 2x^5$ - 5x^4$ + 4x + 3$$?

Accepted Answer

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

Question 13

For $$f(x) = x^2$ + 5x - 6$$, what are the zeros?

Accepted Answer

Question 14

Given $$f(x) = x^3$ - 2x^2$ - 5x + 6$$, use Descartes' Rule of Signs to determine the maximum number of positive real roots.

Accepted Answer

3

Question 15

For the polynomial $$f(x) = x^4$ - 6x^3$ + 5x^2$ - 12$$, what is the degree and leading coefficient?

Accepted Answer

Degree: 4, Leading coefficient: 1

Question 16

Which of the following is the correct factorization for $$f(x) = x^2$ + 5x + 6$$?

Accepted Answer

$$(x+2)(x+3)$$

Question 17

For the rational function $$f(x) = \frac{x^2$-4}{x-2}$$, what is the domain?

Accepted Answer

All real numbers except $$x = 2$$

Question 18

Given $$f(x) = x^3$ - 2x^2$ - 5x + 6$$, what is the sum of the zeros?

Accepted Answer

Question 19

For the polynomial $$f(x) = -3x^4$ + 6x^3$ - 3x^2$ + 2x - 8$$, what is the behavior as $$x 	o -\infty$$?

Accepted Answer

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

Quadratic, Polynomial, and Rational Functions: Precalculus Study Guide

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