Practice Exam II

Key

No Calculator Part

Problem 1:  Graph the following functions

A.  y=1/x

B.  y=root(x)

 

C.  f(x) = x-1 for x<2, 3 for x=2, x-2 for x>2

D.  y=-2|x-3|+1

 

Problem 2:  Determine the intercepts, vertex, and axis of symmetry.  Then use this information to sketch the graph.

y=2x^2-8x+6

Problem 3:  Solve the inequality.

x^2 + 6 >= 7x

Problem 4:  Consider the polynomial below.

f(x) = x(x+1)^2(x-1)^3

A.  List the real zeros and multiplicities

B.  Determine whether the graph crosses or touches the x-axis at each x-intercept.

C.  Determine the maximum number of turning points on the graph.

D.  Determine the behavior.  That is, find the power function that the graph of f resembles for large values of |x|.

Calculator Part

Problem 5:  Shown below is the graph of y = f (x).  Sketch the graph of y = 1/3 f (-x) - 2.

Graph with key points at (-3,1), (0,4), and (6,0)

Problem 6:  A rectangle is inscribed in a semicircle of radius 4 as shown below.  Let P = (x,y) be the point in the first quadrant that is a vertex of the rectangle and is on the circle.

 

Graph of semi circle y = root(16 - x^2) and rectangle

A.  Express the area A of the rectangle as a function of x. 

B.  Express the perimeter p of the rectangle as a function of x.

C.  For what value of x is A the largest?  What is this largest A?

D.  For what value of x is p the largest?  What is the largest p?

 

Problem 7:  The two data sets below represent two different runner's distances (in miles) vs. time (in seconds).  For each of them sketch the graph of the scatter diagram.  Then determine if a linear model or a quadratic model best describes the graph.  Sketch these best fitting curve on the scatter diagram.  If it is a line, interpret the slope.  Then use your model to predict the times of each for a distance of 6 miles.

 
Distance Time    
1 7
1 6
2 15
3 18
5 35
5 38
7 45
7 50
8 57
10 71
 
Distance Time    
1 5
2 12
2 13
3 20
3 21
5 40
7 60
8 82
8 84
10 150

 

Problem 8:  The demand equation for selling x liters of fresh carrot juice at a health food store at a price of p dollars is given by

x(p) = -6p + 50

A.  Find the revenue as a function of p.

B.  What price should the store sell the juice in order to maximize revenue?

C.  Use your calculator's graphing capabilities to determine the range prices that produces a revenue greater than $20.