Q: Which of the following describes the end behavior of $$f(x) = 3(2-x)(x+2)(x-1)^2$?

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

Question 1

Given the piecewise function 
$$\begin{cases} -2x-5, & 	ext{if } -4 \leq x \u003c -2 \ -3(x+1)^2$, & 	ext{if } -2.5 \u003c x \u003c 0 \ |x-1|-5, & 	ext{if } x \geq 0 \end{cases}$$, what is $$f(-3)$$?

Accepted Answer

$$-2(-3)-5 = 1$$

Question 2

For the function $$f(x) = \sqrt{-x+5}$$, what is the domain?

Accepted Answer

$$x \leq 5$$

Question 3

Which of the following describes the end behavior of $$f(x) = 3(2-x)(x+2)(x-1)^2$?

Accepted Answer

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

Question 4

Find the vertex of the quadratic function $$f(x) = -2x^2$ - 12x - 21.$$

Accepted Answer

$$( -3, -3 )$$

Question 5

What is the axis of symmetry for $$f(x) = -2x^2$ - 12x - 21$$?

Accepted Answer

$$x = -3$$

Question 6

Given $$f(x) = \frac{x^2$ + 16}{x^2$ + 5x + 4}$$, what are the vertical asymptotes?

Accepted Answer

$$x = -4$$ and $$x = -1$$

Question 7

For the rational function $$h(x) = \frac{5x^2$ - 6x - 8}{9x^2$ + 5x - 7}$$, what is the horizontal asymptote?

Accepted Answer

$$y = 5/9$$

Question 8

What is the $$y-$$intercept of $$f(x) = \frac{x-6}{3x-7}$$?

Accepted Answer

$$y = -6/7$$

Question 9

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

Accepted Answer

Degree 6

Question 10

Given $$f(x) = \frac{x^2$ + 5x}{x^2$ + 5x - 4}$$, what are the $$x-$$intercepts?

Accepted Answer

$$x = 0$$ and $$x = -5$$

Question 11

For $$f(x) = \frac{x^2$ + x - 30}{x^2$ - x - 42}$$, what is the horizontal asymptote?

Accepted Answer

$$y = 1$$

Question 12

What is the range of $$f(x) = -2x^2$ - 12x - 21$$?

Accepted Answer

$$(-\infty, -3]$$

Question 13

Which of the following is the correct standard form equation for a parabola with vertex at $$(2, 5)$$ and passing through $$(0, 1)$$?

Accepted Answer

$$y = a(x-2)^2$ + 5$$, where $$a = -1$$

Question 14

For $$f(x) = \frac{2x^4$ + 11x^2$ + 5x - 1}{x^4$ + 6x + 5}$$, what is the horizontal asymptote?

Accepted Answer

$$y = 2$$

Question 15

What is the $$y-$$intercept of $$f(x) = 4x - 4x^4$ + 1$$?

Accepted Answer

$$y = 1$$

Question 16

For $$f(x) = \frac{x^3$ + x^2$ - 30}{x^2$ - x - 42}$$, what are the vertical asymptotes?

Accepted Answer

$$x = 7$$ and $$x = -6$$

Question 17

Given $$f(x) = \frac{x^2$ + 5x}{x^2$ + 5x - 4}$$, what is the domain?

Accepted Answer

$$x 
eq 4$$ and $$x 
eq -1$$

Question 18

For $$f(x) = \frac{x^2$ + 16}{x^2$ + 5x + 4}$$, what is the $$y-$$intercept?

Accepted Answer

$$y = 1$$

Question 19

What is the degree and leading coefficient of $$f(x) = 3(2-x)(x+2)(x-1)^2$?

Accepted Answer

Degree 4, Leading Coefficient $$-3$$

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