Download MAT 103 F09 NAME__________________________________

MAT 103 F09
TEST 2 REVIEW
NAME__________________________________
Determine whether the relation represents a function. If it is a function, state the domain and range.
1)
3
6
9
12
6
12
18
24
Circle the correct response:
Function
Not a function
Domain: ____________________________________
Range: __________________________________________
2)
Alice
Brad
Carl
snake
cat
dog
Circle the correct response:
Function
Not a function
Domain: ____________________________________
Range: __________________________________________
3) {(19, -4), (3, -3), (3, 0), (12, 3), (28, 5)}
Circle the correct response:
Function
Not a function
Domain: ____________________________________
Range: __________________________________________
4) {(-4, 20), (-3, 13), (0, 4), (3, 13), (5, 29)}
Circle the correct response:
Function
Not a function
Domain: ____________________________________
Range: __________________________________________
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Determine the domain of the function. Express answer in interval notation.
5) f(x) = - 5x-8
Domain: _____________________________
6) f(x) =
x
x +3
Domain: _____________________________
7) f(x) =
x+ 5
Domain: _____________________________
Provide an appropriate response.
8) A rule that produces a correspondence between two sets of elements such that to each element of the first set
there corresponds one and only one element of the second set is called a ___________________________.
9) In a correspondence between two set, the first set (consisting of the input values) is called the _______________ .
Find the function value.
10) Find f(9) when f(x) = 4 - 8x2.
11) Given that f(x) = 5x 2 - 2x, find f(a - 6). Give answer in simplest form.
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The graph of a function f is given. Use the graph to answer the question.
12) Use the graph of f given below to find f(-25).
25
25
-25
-25
f(-25) = ______________
Provide an appropriate response.
13) If g(x) = -4x2 + x - 9, find:
a) g(-3)
b) g(0)
c) g
1
2
Solve the problem.
14) The function F described by F(x) = 2.75x + 71.48 can be used to estimate the height, in centimeters, of a woman
whose humerus (the bone from the elbow to the shoulder) is x cm long. Estimate the height of a woman whose
humerus is 31.05 cm long. Round your answer to the nearest two decimal places.
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15) The point at which a company's costs equals its revenue is the break-even. C represents cost, in dollars, of x
units of a product. R represents the revenue, in dollars, for the sale of x units. Find the number of units that must
be produced and sold in order to break even. Show work.
C(x) = 15x + 12,000
R(x) = 18x - 6000
16) To estimate the ideal minimum weight of a woman in pounds multiply her height in inches by 4 and subtract
130. Let W = the ideal minimum weight and h = height. Express W as a linear function of h.
W(h) = __________________________________________________________
Choose the appropriate response by circling the letter of your choice.
17) How can the graph of f(x) = -
x - 1 be obtained from the graph of y =
x?
A) Shift it horizontally 1 unit to the right. Reflect it across the x-axis.
B) Shift it horizontally -1 unit to the left. Reflect it across the x-axis.
C) Shift it horizontally 1 unit to the left. Reflect it across the x-axis.
D) Shift it horizontally 1 unit to the left. Reflect it across the y-axis.
Choose the appropriate response.
18) How can the graph of f(x) = -(x + 4 )2 - 6 be obtained from the graph of y = x2 ?
A) Shift it horizontally 4 unit to the right. Reflect it across the y-axis. Shift it 6 units up.
B) Shift it horizontally 4 unit to the right. Reflect it across the y-axis. Shift it 6 units down.
C) Shift it horizontally 4 unit to the left. Reflect it across the x-axis. Shift it 6 units up.
D) Shift it horizontally 4 unit to the left. Reflect it across the x-axis. Shift it 6 units down.
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Provide an appropriate response.
19) The following graph represents the result of applying a sequence of two transformations to the graph of a basic
function. Identify the basic (parent) function and describe the transformation(s). Write the equation for the
given graph.
Equation of parent function: _________________________
Transformations:
Equation for given graph: ___________________________________________________________
Write an equation for a function that has a graph with the given transformations.
20) The graph of y =
x is shifted 3 units to the left. Then the graph is shifted 9 units upward.
Equation of transformed function: _____________________________________
21) The graph of y = x3 is vertically stretched by a factor of 5, and the resulting graph is reflected across the x-axis.
Equation of transformed function: _____________________________________
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22) Given the function y = - x-1 +3,
a) Write the equation of the parent function: ______________________________
b) List the transformations that the graph of the parent function must undergo to obtain the graph of the given
function.
c) Sketch the graph of the given function.
d) State the domain and range of the given function using interval notation.
Domain: _________________________
Range: ____________________________
Create a table of values and then graph the piecewise function.
23)
f(x) =
x+5
3
if x < 1
if x 1
6
Answer the following question using algebraic methods.
24) For the parabola with equation f(x) = 4x2 - 32x + 63, find:
a) The equation of the axis of symmetry
b) The coordinates of the vertex.
Determine whether there is a maximum or minimum value for the given function, and find that value.
25) f(x) = -x2 + 20x -104
Max or min? __________________
Value: _______________
26) f(x) = x 2 + 18x + 90
Max or min? __________________
Value: _______________
Find the range of the given function. Express your answer in interval notation.
27) f(x) = 4x2 + 16x + 19
Range: ____________________
28) f(x) = -(x + 7)2 -2
Range: ____________________
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29) Given the function f(x) = x2 - 3x - 4, complete the followingusing algebraic methods. SHOW ALL WORK.
a) Does the parabola open upward or downward? _____________________
b) Find the equation of the axis of symmetry. __________________________
c) Find the coordinates of the vertex. _________________________________
d) Find the y-intercept. Write the answer as an ordered pair. ______________________
e) Find the x-intercepts of the graph, if any. Write the answer(s) as ordered pairs. ________________________
f) Use your answers from parts a - e to neatly graph the parabola on the axes below. Sketch the axis of
symmetry as a dotted line. Label the vertex and the intercepts.
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Write the function.
30) In economics, functions that involve revenue, cost and profit are used. Suppose R(x) and C(x) denote the total
revenue and the total cost, respectively, of producing a new high-tech widget. The difference P(x) = R(x) - C(x)
represents the total profit for producing x widgets.
a) Given R(x) = 60x - 0.4 x2 and C(x) = 3x + 10, find the equation for P(x). Expess the function in simplest form.
b) Graph the profit function on your calculator and determine the number of widgets that must be produced in
order to maximize the profit. What is the maximum profit? Round answers to nearest whole number.
Use the REGRESSION feature on a graphing calculator.
31) The average retail price in the Spring of 2000 for a used Camaro Z28 coupe depends on the age of the car as
shown in the following table.
Age, x
1
2
3
4
5
6
7
8
9
Price, y 18,325 15,925 13,685 11,805 10,490 8885 8015 6480 5710
Find the quadratic model that best estimates this data. Round your answer to whole numbers.
y = ________________________________________________________________
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32) As the number of farms has decreased in South Carolina, the average size of the remaining farms has grown
larger, as shown below.
YEAR
1900 (x = 0)
1910 (x = 10)
1920
1930
1940
1950
1960
1970
1980
1990
AVERAGE ACREAGE
PER FARM
127
119
122
137
155
196
283
353
406
460
Let x represent the number of years since 1900.
a) Use a graphing calculator to view the scatterplot of the data.
b) Use a graphing calculator to fit a quadratic function to the data. Round your answer to five decimal places.
y = _______________________________________________________________________________________
c) Use your model (regression equation) from part b) to estimate the average acreage per farm in 1947. Round to
the nearest whole number.
d) Should we use this model to predict the acreage per farm in 2009? Explain.
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