Exam 1 Review Sp16 O’Brien
CA 6th HLR
Exam 1 Review: 1.1 – 2.6
Directions:
1.
Try to work the following problems with your book, notes, and homework closed. You may have
your graphing calculator and some blank paper. The idea is to practice working problems with no
resources other than what you will have during the exam. This is will help you to identify your
weak areas where you need further study. If you miss a problem, practice working some
problems like it with your book, notes, and homework open. Then work a few similar problems
with your resources closed. Get in the habit of showing all of your support work on every
problem.
Find the length of the unknown side of the right triangle. a and b represent the lengths of the legs and
c represents the length of the hypotenuse.
b  7 , c  11 ; find a
2.
1.1.84
Find a) the distance between P and Q and b) the midpoint of the line segment joining P and Q.
P(8.9, 1.6), Q(3.9, 13.6)
1.1.94
3.
Determine the domain D and range R of the given relation and tell whether it is a function.
1.2.36
4.
Use the graph of y = f(x) to find each function value: a) f(–2) b) f(0) c) f(1) d) f(4).
1.2.76
5.
Graph the linear function: f x  
6.
By noon, 3 inches of rain had fallen during a storm. Rain continued to fall at a rate of
2
x2.
1.3.4
3
Give the a) x-intercept, b) y-intercept, c) domain, d) range, e) slope of the line. Do not use a calculator.
a.
1
inch per hour.
4
Find a formula for a linear function f that models the amount of rainfall x hours past noon.
b.
Find the total amount of rainfall by 2:30 p.m.
1.3.87
7.
Find the slope-intercept form of the equation of the line through (–1, 6.25) and (2, –4.25).
Do not use a calculator.
1.4.20
Graph the line 4x – 3y = 9 by hand. Give the x- and y-intercepts.
1.4.32
8.
1
Exam 1 Review Sp16 O’Brien
CA 6th HLR
9.
10.
Write the equation of the line satisfying the given conditions, giving it in slope-intercept form,
if possible.
a) Through (–2, 0), perpendicular to 8x – 3y = 7
1.4.46
b) Through (–5, 8), parallel to y = –.2x + 6
1.4.49
A person is riding a bicycle along a straight highway.
The graph at the right shows the rider’s distance y in
miles from an interstate highway after x hours.
a) Find the slope-intercept form of the line.
b) How fast is the biker traveling?
c) How far was the biker from the interstate highway
initially?
d) How far was the biker from the interstate highway
after 1 hour and 15 minutes?
11.
1.4.61
Worldwide gambling revenue from online betting was $18 billion in 2007 and $24 billion in 2010.
a) Write the equation of a line y= mx + b that models this information, where y is in billions of
dollars and x is the year.
b) Use this equation to estimate online betting revenue in 2013.
12.
1.4.63
The following table lists the average tuition and fees(in constant 2010 dollars) at public colleges and
universities for selected years.
1.4.70
Year
1980
1990
2000
2005
2010
Tuition & Fees
5938
7699
9390
11,386
13,297
a) Use regression to find a formula f(x) = mx + b so that f models the data.
b) Use the model to predict tuition and fees in 2016.
13.
14.
Find the zero of the function f. Do not use a calculator.
f(x) = 1.5x + 2(x – 3) + 5.5(x + 9)
1.5.9
Solve the following equation analytically.
1.5.38
3 1
1 4
 x  x
4 5
2 5
15.
Classify the following equation as a contradiction, an identity, or a conditional equation.
Give the solution set.
1.5.57
–4 [6 – (–2 + 3x)] = 21 + 12x
16.
Solve the following inequality analytically. Write the solution set in interval notation.
1.5.94
2x  3 3x  1
4x  7


5
2
2
Use algebra to solve the following applications, not just trial and error or “common sense”.
17.
The length of a rectangular mailing label is 3 cm less than twice the width. The perimeter is 54 cm.
Find its dimensions.
1.6.10
2
Exam 1 Review Sp16 O’Brien
CA 6th HLR
18.
At 2:00 p.m. a runner heads north on a highway, jogging at 10 mph. At 2:30 p.m. a driver heads north
on the same highway to pick up the runner. If the car travels at 55 mph, how long will it take the driver
to catch the runner?
1.6.18
19.
How many gallons of a 5% acid solution must be mixed with 5 gallons of a 10% solution to
obtain a 7% solution?
20.
1.6.19
A baker makes cakes and sells them at county fairs. Her initial cost for the Benton County Fair was
$40.00. She figures each cake cost $2.50 to make and she charges $6.50 per cake. Let x represent
the number of cakes sold and assume no cakes are leftover.
a) Express the total cost C as a function of x.
b) Express the revenue R as a function of x.
c) Determine analytically the value of x for which revenue equals cost.
1.6.36
21.
Nancy B. Kindy won $200,000 in a state lottery. She first paid income tax of 30% on the winnings.
Of the rest, she invested some at 1.5% and some at 4%, earning $4350 interest per year. How
much did she invest at each rate?
1.6.79
22.
Solve the formula for the specified variable.
1.6.63
P = 2L + 2W for W
23.
Determine the largest open intervals of the domain over which each function is
2.1.18
a) increasing; b) decreasing; and c) constant. Then give the d) domain; and e) range.
24.
Write the equation that results in the desired translation. Do not use a calculator.
The squaring function, shifted 1000 units to the left and 255 units downward.
25.
26.
27.
28.
2.2.14
Without a graphing calculator, determine the domain and range of the following function.
f(x)  (x  1)2  5
2.2.37
Use translations of one of the basic functions to sketch the graph of y  x  3  4 .
Do not use a calculator.
2.2.50
Write the equation that results in the desired transformations.
Do not use a calculator.
The square root function, vertically shrunk by applying a factor of .2 and reflected
across the x-axis.
2.3.8
Describe the series of transformations applied to y  x that would result in the graph of
2.3.29
y
1
x  2  3 . Be specific about direction and magnitude. [Note the change in directions.]
4
3
Exam 1 Review Sp16 O’Brien
CA 6th HLR
29.
Give the equation of the function whose graph is described below.
2.3.36
The graph of y  3 x is shifted 2 units to the left. This is then vertically stretched by applying
a factor of 1.5. Finally, the graph is shifted 8 units upward.
30.
31.
The adjacent figure shows a transformation of the graph of y  x .
Write the equation for the graph.
2.3.92
The graph of y = f(x) represents the amount of water
in thousands of gallons remaining in a swimming pool
after x days.
2.5.3
a) Estimate the initial and final amounts of water
contained in the pool.
b) When did the amount of water in the pool remain
constant?
c) Approximate f(2) and f(4).
d) At what rate was water being drained from the pool
when 1  x  3 ?
32.
Graph the following piecewise-defined function. Is f continuous on its domain?
Do not use a calculator.
4  x
f(x)  
1  2x
33.
2.5.11
for x  2
for x  2
Given f(x) = 9 – 2x and g(x) = –5x + 2, find the following. Do not use a calculator.
2.6.24
a) (f + g)(x), (f – g)(x), (fg)(x);
b) the domains of the functions in part a;
c)
f
and give its domain;
g
d) f  g and give its domain;
e) g  f and give its domain
34.
Find the difference quotient,
f x  h  f x 
(where h  0 ) for f(x) = x2 + 2x.
h
2.6.86
Simplify completely.
35.
An oil well off of the Gulf Coast is leaking, with the leak spreading oil over the water’s
surface as a circle. At any time t, in minutes, after the beginning of the leak, the radius
of the circular oil slick on the surface is r t   3t feet. Let Ar   π r 2 represent the area of
a circle of radius r.
2.6.106
a) Find A  r t  .
b) The answer to part a defines the ____________________ in terms of ____________________.
c) What is the area of the oil slick after 5 minutes?
4
Exam 1 Review Sp16 O’Brien
CA 6th HLR
Answers
1.
a=2
2.
a) d = 13 b) M = (6.4, 7.6)
3.
D:  ,   ; R:  , 4 ; Function
4.
a) 5; b) 0; c) 2; d) 4
5.
a) (3, 0); b) (0, –2); c) D:  ,   ; d) R:  ,   ; e) m 
6.
a) f(x) 
7.
y = –3.5x + 2.75
8.
9 
 , 0  ; (0, –3)
4 
9a.
3
3
y  x
8
4
9b.
y = –.2x + 7
10.
a) y = 11x + 117;
b) 11 mph;
11.
a) y = 2x – 3996
b) $30 billion
12.
a) y  236.6897x  463,127
13.

14.
5
12
15.
contradiction;
16.
 24 
, 

 31 
17.
length: 17 cm; width: 10 cm
18.
1
hr
9
19.
7.5 gallons
20.
a) C(x) = 2.50x + 40; b) R(x) = 6.50x; c) 10
2
3
1
x  3 ; b) 3.625 in.
4
c) 117 mi.;
d) 130.75 mi.
b) $14,039
29
6
5
Exam 1 Review Sp16 O’Brien
CA 6th HLR
P
L
2
W
22.
$50,000 at 1.5% and $90,000 at 4%
23.
a)
24.
y = (x + 1000)2 – 255
25.
D: (, ) ; R:  5,  
26.
Base function: y  x ; shifted 3 left and 4 down
27.
y  .2 x
28.
shift right 8; vertically shrink by a factor of
29.
y  1.5 3 x  2  8
30.
y
31.
a) 50,000 gal; 30,000 gal;
4,   ;
or
b)
W
1
P L
2
21.
 ,  1 ;
c)
 1, 4 ;
d)
 ,   ;
e) 3, 
1
; reflect over the x-axis; shift up 3
4
1
x 1  2
2
b) during the first & fourth days;
c) 45 thousand; 40 thousand;
d) 5000 gal per day
32.
Not continuous.
33.
a) (f + g)(x) = –7x + 11; (f – g)(x) = 3x + 7; (fg)(x) = 10x2 – 49x + 18
b) Domain is  ,   for all three functions.
f
9  2x
2 2 

c)  x  
; D:   ,    ,  
g

5x

2
5

 5 
 
d)
e)
f  gx   10x  5 ; D:  ,  
g  f x  10x  43 ; D:  ,  
34.
f x  h  f x 
= 2x + h + 2
h
35.
a)
A  r t   4π t 2
b) area; time
c) 64π mi 2
6