Exam
Name___________________________________
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Solve the problem.
1)
An electric company has the following rate schedule for electricity usage in single–family
residences:
Monthly service charge $4.93
Per kilowatt service charge
1st 300 kilowatts $0.11589/kW
Over 300 kilowatts $0.13321/kW
What is the charge for using 300 kilowatts in one month?
What is the charge for using 375 kilowatts in one month?
Construct a function that gives the monthly charge C for x kilowatts of electricity.
1)
2)
One Internet service provider has the following rate schedule for high–speed Internet
service:
Monthly service charge $18.00
1st 50 hours of use free
Next 50 hours of use $0.25/hour
Over 100 hours of use $1.00/hour
What is the charge for 50 hours of high–speed Internet use in one month?
What is the charge for 75 hours of high–speed Internet use in one month?
What is the charge for 135 hours of high–speed Internet use in one month?
2)
3)
A gas company has the following rate schedule for natural gas usage in single–family
residences:
Monthly service charge $8.80
Per therm service charge
1st 25 therms $0.6686/therm
Over 25 therms $0.85870/therm
What is the charge for using 25 therms in one month?
What is the charge for using 45 therms in one month?
Construct a function that gives the monthly charge C for x therms of gas.
3)
4)
A cellular phone plan had the following schedule of charges:
Basic service, including 100 minutes of calls $20.00 per month
2nd 100 minutes of calls $0.075 per minute
Additional minutes of calls $0.10 per minute
What is the charge for 200 minutes of calls in one month?
What is the charge for 250 minutes of calls in one month?
Construct a function that relates the monthly charge C for x minutes of calls.
4)
5)
The wind chill factor represents the equivalent air temperature at a standard wind speed
that would produce the same heat loss as the given temperature and wind speed. One
formula for computing the equivalent temperature is
W(t) =
t
33 –(10.45 + 10 v– v)(33 – t )
22.04
33 – 1.5958(33 – t)
if 0
v < 1.79
if 1.79
v < 20
if v 20
where v represents the wind speed (in meters per second) and t represents the air
temperature (°C). Compute the wind chill for an air temperature of 15°C and a wind speed
of 12 meters per second. (Round the answer to one decimal place.)
5)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Determine the slope and the y–intercept of the graph of the equation.
6)
x +15y –1 = 0
A)
m = 1; (0, 1)
B)
m =1
15 ; 0, 1
15
C)
m = – 1
15 ; 0, 1
15
D)
m = – 15; (0, 15)
Write the standard form of the equation of the circle with the given center and radius.
7)
(0, 0); 9
A)
x2+y2=81
B)
x2+y2=18
C)
x2–y2=9
D)
x2+y2=9
Graph the linear function by plotting the x– and y–intercepts.
8)
0.3x + 0.4y –2.4 = 0
A)
intercepts: (0, –6), (8, 0)
B)
intercepts: (0, 6), (8, 0)
3
C)
intercepts: (0, –6), (–8, 0)
D)
intercepts: (0, 6), (–8, 0)
Find and simplify the difference quotient f(x +
h) – f(x)
h, h
0 for the given function.
9)
f(x) =3x – 7
A)
3
B)
3+6(x – 7)
h
C)
3+
–14
h
D)
0
Determine which two functions are inverses of each other.
10)
f(x) =x3–11 g(x) =
3x –11 h(x) =x3+11
10)
A)
g(x) and h(x)
B)
None
C)
f(x) and h(x)
D)
f(x) and g(x)
Evaluate the function at the given value of the independent variable and simplify.
11)
f(x) =3x2– 3x – 4;f(x – 1)
11)
A)
–9x2+ 3x + 2
B)
3x2– 15x – 4
C)
3x2– 9x – 4
D)
3x2– 9x + 2
Begin by graphing the square root function f(x) =x Then use transformations of this graph to graph the given function.
4
12)
g(x) =2x +5
12)
A)
B)
C)
D)
5
Based on the graph, find the range of y = f(x).
13)
f(x) =
–1
2xif x
0
–7if x = 0
13)
A)
(–, )
B)
(–, 0) or {0} or (0, )
C)
(–10, 10)
D)
(–, 0) or (0, )
Write the standard form of the equation of the circle with the given center and radius.
14)
(0, 0); 14
14)
A)
x2+y2=14
B)
x2+y2=14
C)
x2+y2=7
D)
x2+y2=196
B
Determine whether the relation is a function.
15)
{(–6, –5), (–3, –7), (4, 6), (4, 8)}
15)
A)
Not a function
B)
Function
A
Graph the given functions on the same rectangular coordinate system. Describe how the graph of g is related to the graph
of f.
6
D
16)
f(x) =x, g(x) =x–2
16)
A)
g shifts the graph of f vertically up 2units
B)
g shifts the graph of f vertically down 2units
7
C)
g shifts the graph of f vertically down 2units
D)
g shifts the graph of f vertically up 2units
Use the vertical line test to determine whether or not the graph is a graph in which y is a function of x.
17)
17)
A)
not a function
B)
function
Given functions f and g, determine the domain of f +
g.
18)
f(x) =4x – 5,g(x) =3x + 3
18)
A)
(0, )
B)
(–, –4) or (–4, )
C)
(–, )
D)
(–, 0) or (0, )
C
Begin by graphing the standard absolute value function f(x) =x. Then use transformations of this graph to graph the
given function.
19)
g(x) =1
3x – 2 + 5
19)
9
B
A)
B)
C)
D)
Determine which two functions are inverses of each other.
20)
f(x) =x – 3
2g(x) =2x – 3 h(x) =x + 3
2
20)
A)
f(x) and h(x)
B)
g(x) and h(x)
C)
None
D)
f(x) and g(x)
Determine whether the relation is a function.
21)
{(–2, –9), (3, –5), (6, 6), (8, 1), (11, 2)}
21)
A)
Function
B)
Not a function
Use the vertical line test to determine whether or not the graph is a graph in which y is a function of x.
22)
22)
A)
not a function
B)
function
Evaluate the piecewise function at the given value of the independent variable.
23)
h(x) =
x2– 7
x + 6 if x –6
x – 2 if x = – 6
; h(–6)
23)
A)
8
B)
–4
C)
undefined
D)
–8
D
Find the midpoint of the line segment whose end points are given.
24)
(4, 6) and (5, 1)
24)
A)
(9
2, 7
2)
B)
(9, 7)
C)
(–1, 5)
D)
(–1
2, 5
2)
A
B
Use the given conditions to write an equation for the line in the indicated form.
25)
Passing through (4, 5) and perpendicular to the line whose equation is y =4x + 7;
point–slope form
25)
A)
y –4=1
4(x –5)
B)
y = – 4x – 24
C)
y –5= – 1
4(x –4)
D)
y –5=1
4(x +4)
Does the graph represent a function that has an inverse function?
26)
26)
A)
No
B)
Yes
Begin by graphing the standard square root function f(x) =x . Then use transformations of this graph to graph the given
function.
27)
g(x) =x – 2 + 4
27)
12
A)
B)
C)
D)
Use the given conditions to write an equation for the line in slope–intercept form.
28)
Slope =2, passing through (–6, 3)
28)
A)
y – 3 =2x + 6
B)
y =2x + 15
C)
y – 3 = x + 6
D)
y =2x – 15
Identify the intervals where the function is changing as requested.
29)
Decreasing
29)
A)
(–, –2)
B)
(–, –3)
C)
(–3, –2)
D)
(0, –2)
Identify the intercepts.
30)
30)
A)
(0, –6)
B)
(6, 0), (–6, 0), (0, 0)
C)
(6, 0), (–6, 0), (0, –6)
D)
(6, 0), (–6, 0)
C
C
Solve.
31)
A vendor has learned that, by pricing hot dogs at $1.75, sales will reach 128 hot dogs per day.
Raising the price to $2.50 will cause the sales to fall to 98 hot dogs per day. Let y be the number of
hot dogs the vendor sells at x dollars each. Write a linear equation that models the number of
hot dogs sold per day when the price is x dollars each.
31)
A)
y = – 1
40 x +20473
160
B)
y = – 40x +198
C)
y = – 40x –198
D)
y =40x + 58
Find the average rate of change of the function from x1 to x2.
32)
f(x) =2x from x1= 2 to x2= 8
32)
A)
7
B)
–3
10
C)
2
D)
1
3
D
Use the given conditions to write an equation for the line in point–slope form.
33)
Slope =5
6, passing through (3, 5)
33)
A)
y =5
6x + 3
B)
y + 5 =5
6(x + 3)
C)
x – 5 =5
6(y – 3)
D)
y – 5 =5
6(x – 3)
D
Given functions f and g, determine the domain of f +
g.
34)
f(x) =3x2– 1, g(x) =2x3+ 8
34)
A)
(–, –3) or (–3, –2) or (–2, )
B)
(0, )
C)
(–, 0) or (0, )
D)
(–, )
D
15
B
Use the graph to find the indicated function value.
35)
y = f(x). Find f(5)
35)
A)
11
B)
–11
C)
9
D)
2
Determine the slope and the y–intercept of the graph of the equation.
36)
x + y – 2 = 0
36)
A)
m = – 1; (0, 2)
B)
m = – 1; (0, –2)
C)
m = 1; (0, 2)
D)
m = 0; (0, 2)
16
Solve.
37)
A school has just purchased new computer equipment for $25,000.00. The graph shows the
depreciation of the equipment over 5 years. The point (0, 25,000) represents the purchase price and
the point (5, 0) represents when the equipment will be replaced. Write a linear equation in
slope–intercept form that models the value of the equipment, y, x years after purchase. Use the
model to predict the value of the equipment after 4 years?
37)
A)
y =5000x –25,000;
value after 4 years is $5000.00
B)
y = – 5000x +25,000;
value after 4 years is $5000.00;
C)
y =25,000x + 5;
value after 4 years is $5000.00
D)
y = – 25,000x +25,000;
value after 4 years is $–75,000.00
Find the domain of the function.
38)
f(x) =
–4x
x + 8
38)
A)
(–, –8)
(–8, )
B)
(–, –8)
C)
(–, )
D)
(–, 0)
(0, )
A
Use the graph of the function f, plotted with a solid line, to sketch the graph of the given function g.
39)
g(x) = f(x – 1)
y = f(x)
39)
17
B
A)
B)
C)
D)
Use the given conditions to write an equation for the line in the indicated form.
40)
Passing through (5, –4) and parallel to the line whose equation is y = – 2x + 3 ;
point–slope form
40)
A)
y –5= – 2(x + 4)
B)
y + 4 = – 2(x –5)
C)
y + 4 = x –5
D)
y = 2x
For the given functions f and g , find the indicated composition.
41)
f(x) =5x + 15,g(x) =5x – 1
(f
g)(x)
41)
A)
25x + 20
B)
25x + 74
C)
25x + 10
D)
25x + 14
Begin by graphing the standard cubic function f(x) =x3. Then use transformations of this graph to graph the given
function.
18
42)
g(x) =1
2x3
42)
A)
B)
C)
D)
Determine whether the relation is a function.
43)
{(–4, –4), (–2, 1), (–1, –7), (5, –9)}
43)
A)
Not a function
B)
Function
B)
Graph the function.
19
B)
44)
f(x) =–x + 3 if x < 2
2x – 3 if x
2
44)
A)
B)
C)
D)
20