College Algebra
Unit 2 Study Guide – Take Home Quiz
Name
Directions: Show all work and reasoning to receive full credit.
For Questions 1 & 2, determine the domain of the functions. Answers should be in interval notation.
x4
1) h( x)  3
2) g ( x)  3  7 x
x  4x
3) For the given functions f and g, find the following functions and the domain of each:
𝑓(𝑥) =
a) f + g
2𝑥 + 3
;
3𝑥 − 2
b) f – g
4) Determine and simplify the difference quotient f,
𝑔(𝑥) =
4𝑥
3𝑥 − 2
c) f ● g
d)
𝑓
𝑔
f ( x  h)  f ( x )
, h  0 , given f ( x)  2 x2  9 x  5 .
h
5) Answer the following questions about the function f (x) 
3x  6
x2  4
5
a) If f (x)  , what is x? What are the point(s) on the graph?
3


b) List the x-intercepts and y-intercept, if any, of the graph of f. Check your answers.
For Questions 1 & 2, determine algebraically whether the function is even, odd, or neither. Then state any
symmetry.
 x3
3
6) f ( x)  2
7) g ( x)  3 x 2  8
4x  9
8) Use the graph to the right to answer the following questions a - f.
a) Determine the interval when the function is
increasing.
b) Determine the interval where the function is
constant.
c) Determine the interval where the function is decreasing.
d) List the intercepts (x, y) for the function.
e) Find f(3).
f) For what value of x does f(x) = -2?
9) Find the average rate of change of the function f (x) 
x3
from -3 to 2 (no decimal approximations).
x2  3

10) Use the function f ( x)  x 2  7 x to answers questions a and b.
a) Find the average rate of change from -1 to x.
b) Find the equation of the secant line in slope intercept form containing (-1, f(1)) and (2, f(2)).
11) Write a rule for the piecewise function graphed.



f ( x)  



1
1
13) Graph by hand the following function.
List the sequence of transformations.
1
f ( x)   x  2  3
2
1
12) Graph the given piecewise function.
 1
 2 x  2, (, 2]

 1
f ( x)   x 2  3, (2, 4]
 2
 3x  13, (4, )


1
14) Graph by hand the following function.
List the sequence of transformations.
g ( x)  2  x  3  1
1
1
1
1
15) Determine the equation of the following graph.
16) Determine the equation of the following graph.
1
1
1
1
17) A wire of length 5x is bent into the shape of a square. Express the area as a function of x.
18) A marina owner wishes to estimate a linear function that relates boat length in feet and its draft (depth of
boat below water line) in feet. He collects the following data. Let boat length represent the independent
variable and draft represent the dependent variable. Use a graphing utility to draw a scatter plot and to find the
line of best fit. Use the equation to determine the draft for a boat 60 ft in length (to the nearest thousandth).
Boat Length (ft)
25
25
30
30
45
45
50
50
Draft (ft)
2.5
2
3
3.5
6
7
7
8
19) An open box is made from a rectangular piece of material by cutting equal squares from each corner and
turning up the sides.
a) Write the volume of the box as a function of x if the
material is 24 inches by 16 inches (use function
notation). Simplify and write your equation in standard
form.
b) Graph the function on your calculator. Determine the value of x that will maximize the volume of the
box. _________________
20) Suppose that a company has just purchased a new machine for its manufacturing facility for $120,000. The
company chooses to depreciate the machine using the straight-line method over 12 years. This means that the
machine will depreciate $12,000 per year.
a) Write a linear function that expresses the book value of the machine as a function of its age.
b) Graph the linear function on your calculator. Sketch the graph (label your axis with the window you
chose to use).
c) What is the book value of the machine after 4 ¾ years? ______________
d) When will the machine be worth $60,000? (show work)