Q: Given $$f(x) = -2x^2$(x-3)^2(x+1)^2$, what is the end behavior of the function?

As $$x \to \pm\infty$$, $$f(x) \to -\infty$$

Question 1

Given the piecewise function

$$\begin{cases}
-2x-5, & 	ext{if } -4.5 \u003c x \u003c -2 \
-3(x+1)^2$, & 	ext{if } -2.5 \u003c x \u003c 0 \
|x-1|-5, & 	ext{if } x \geq 0
\end{cases}$$

What is the value of $$f(-3)$$?

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 transformation applied to $$f(x) = |x| to $$obtain $$f(x) = \frac{1}{2}|x-7|-4$$?

Accepted Answer

Shift right 7 units, vertical stretch by $$\frac{1}{2}$$, shift down 4 units

Question 4

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

Accepted Answer

4

Question 5

For the function $$f(x) = -2x^2$ - 12x - 21$$, what is the vertex?

Accepted Answer

$$( -3, -3 )$$

Question 6

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

Accepted Answer

$$x = -3$$

Question 7

Find the $$y-$$intercept of $$f(x) = \frac{x-6}{3x-7}.$$

Accepted Answer

$$y = -6/7$$

Question 8

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

Accepted Answer

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

Question 9

Given $$f(x) = 2x^2$ - 3\sqrt{x-3} - 5$$, what is the domain?

Accepted Answer

$$x \geq 3$$

Question 10

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

Accepted Answer

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

Question 11

For the function $$f(x) = 4x - 8x + 11$$, what is the $$y-$$intercept?

Accepted Answer

$$y = 11$$

Question 12

Given $$f(x) = -2x^2$(x-3)^2(x+1)^2$, what is the end behavior of the function?

Accepted Answer

As $$x 	o \pm\infty$$, $$f(x) 	o -\infty$$

Question 13

For the rational function $$f(x) = \frac{x^3$ + x^2$ - 30}{x^2$ - x - 42}$$, what is the horizontal asymptote?

Accepted Answer

No horizontal asymptote

Question 14

Given $$f(x) = \frac{5x^2$ - 6x - 8}{9x^2$ + 5x - 7}$$, what is the equation of the horizontal asymptote?

Accepted Answer

$$y = \frac{5}{9}$$

Question 15

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

Accepted Answer

$$y = 2$$

Question 16

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

Accepted Answer

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

Question 17

A medical researcher models the spread of a virus using $$f(x) = 3(2-x)(x+2)(x-1)^2$. What is the multiplicity of the x$-intercept at x=1$?

Accepted Answer

2

Question 18

A chemical reaction rate is modeled by $$f(x) = \sqrt{-x+5}. $$What is the maximum value of $$x$$ for which the reaction rate is defined?

Accepted Answer

$$x = 5$$

Question 19

A company models its profit with $$f(x) = 2x^2$ - 3\sqrt{x-3} - 5. $$What is the minimum value of $$x$$ for which the profit function is defined?

Accepted Answer

$$x = 3$$

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