1. Multiple Choice  The function $f ( x) =x^{2}$ is [(a) increasing, (b) decreasing, (c) neither] on the interval $( 0,\infty )$.

2. True or False  The floor function $f( x) =\lfloor x\rfloor$ is an example of a step function.

3. True or False  The cube function is odd and is increasing on the interval $( -\infty ,\infty )$.

4. True or False  The cube root function is odd and is decreasing on the interval $( -\infty ,\infty )$.

5. True or False  The domain and the range of the reciprocal function are all real numbers.

6. A number $r$ for which $f( r) =0$ is called a(n) _____ of the function $f$.

7. Multiple Choice  If $r$ is a zero of even multiplicity of a function $f$, the graph of $f$ [(a) crosses, (b) touches, (c) doesn't intersect] the $x$-axis at $r$.

8. True or False  The $x$-intercepts of the graph of a polynomial function are called zeros of the function.

9. True or False  The function $f( x) =\left[ x+\sqrt[5]{x^{2}-\pi }\right] ^{2/3}$ is an algebraic function.

10. True or False  The domain of every rational function is the set of all real numbers.

23

19. If $f( x) = \lfloor 2x\rfloor$, find

    1. (a) $f( 1.2)$,
    2. (b) $f( 1.6)$,
    3. (c) $f( -1.8)$.

20. If $f( x) =\left\lceil \dfrac{x}{2}\right\rceil$, find

    1. (a) $f( 1.2)$,
    2. (b) $f ( 1.6)$,
    3. (c) $f ( -1.8)$.

21. $f( x) =3( x-7) (x+4) ^{3}$

22. $f( x)=4x( x^{2}+1) ( x-2) ^{3}$

23. 1. (a) $f( x) =-4x ( x-1) ( x-2)$
    2. (b) $f( x) =x^{2} ( x-1) ^{2} ( x-2)$
    3. (c) $f( x) =3x( x-1) ( x-2)$
    4. (d) $f( x) =x( x-1) ^{2}( x-2) ^{2}$
    5. (e) $f( x) =x^{3}( x-1) ( x-2)$
    6. (f) $f( x) =-x ( 1-x ) ( x-2 )$

    

24. 1. (a) $f( x) =2x^{3}( x-1) ( x-2) ^{2}$
    2. (b) $f( x) =x^{2}( x-1) ( x-2)$
    3. (c) $f( x) =x^{3}( x-1) ^{2}( x-2)$
    4. (d) $f( x) =x^{2} ( x-1 ) ^{2} ( x-2 ) ^{2}$
    5. (e) $f( x) =5x( x-1) ^{2}( x-2)$
    6. (f) $f( x) =-2x ( x-1) ^{2} ( 2-x)$

    

25. $R( x) =\dfrac{5x^{2}}{x+3}$

26. $H( x) =\dfrac{-4x^{2}}{( x-2) ( x+4) }$

27. $R( x) =\dfrac{3x^{2}-x}{x^{2}+4}$

28. $R( x) =\dfrac{3(x^{2}-x-6) }{4( x^{2}-9) }$

29. Constructing a Model  The rectangle shown in the figure has one corner in quadrant I on the graph of $y=16-x^{2}$, another corner at the origin, and corners on both the positive $y$-axis and the positive $x$-axis. As the corner on $y=16-x^{2}$ changes, a variety of rectangles are obtained.

    1. (a) Express the area $A$ of the rectangles as a function of $x$.
    2. (b) What is the domain of $A$?

    

30. Constructing a Model  The rectangle shown in the figure is inscribed in a semicircle of radius $2$. Let $P=( x,y)$ be the point in quadrant I that is a vertex of the rectangle and is on the circle. As the point $( x,y)$ on the circle changes, a variety of rectangles are obtained.

    1. (a) Express the area $A$ of the rectangles as a function of $x$.
    2. (b) Express the perimeter $p$ of the rectangles as a function of $x$.

    

31. Height of a Ball A ballplayer throws a ball at an inclination of $45^\circ$ to the horizontal. The following data represent the height $h$ (in feet) of the ball at the instant that it has traveled $x$ feet horizontally:

    Distance, $x$	20	40	60	80	100	120	140	160	180	200
    Height, $h$	25	40	55	65	71	77	77	75	71	64

    1. (a) Draw a scatter plot of the data. Comment on the type of relation that may exist between the two variables.
    2. (b) Use technology to verify that the quadratic function of best fit to these data is $$h( x) =-0.0037x^{2}+1.03x+5.7$$ Use this function to determine the horizontal distance the ball travels before it hits the ground.
    3. (c) Approximate the height of the ball when it has traveled 10 feet.

32. Educational Attainment The following data represent the percentage of the U.S. population whose age is $x$ (in years) who did not have a high school diploma as of January 2011:

    Age, $x$	$30$	$40$	$50$	$60$	$70$	$80$
    Percentage without a High School Diploma, $P$	$11.6$	$11.7$	$10.4$	$10.4$	$17.0$	$24.6$

    Source: U.S. Census Bureau.

    1. (a) Draw a scatter plot of the data, treating age as the independent variable. Comment on the type of relation that may exist between the two variables.
    2. (b) Use technology to verify that the cubic function of best fit to these data is $$P( x) =0.00026x^{3}-0.0303x^{2}+1.0877x-0.5071$$
    3. (c) Use this model to predict the percentage of 35-year-olds who do not have a high school diploma.