Practice Problems for Exam 1
Math 140A, Summer 2014,
July 2
Name:
INSTRUCTIONS: These problems are for PRACTICE. For the practice
exam, you may use your book, consult your classmates, and use any other
resource available. For the actual exam, calculators will not be allowed.
The actual exam will also be shorter, to allow all work to be done within an
hour. These problems are for practice only.
Section 2.2
Question 1 Find the intercepts and graph the equation below by plotting points. Be
sure to label the intercepts.
y = x2 − 5x + 6
Question 2 Test the following equation for symmetry with respect to the x-axis, the
y-axis, and the origin.
y 4 + x3 − 5x = 0
Section 2.3
Question 3 Find the point-slope form of the equation of the line which contains the
points (−4, 2) and (5, −4). Graph the line.
Question 4 Find the slope-intercept form of the equation of the line which contains
the point (−2, 6) and has a slope of −5. Graph the line.
Question 5 Find the equation of the line with a slope of 0 which contains the point
(−7, 3). Graph the line.
Question 6 Find the equation of the line with undefined slope which contains the point
(−7, 3). Graph the line.
Section 2.4
Question 7 Find the standard form of the equation of the circle
x2 + y 2 − 16x − 4y + 52 = 0.
List the center and the radius of the circle. Graph the circle. Label the center and at
least one point on the circle.
Question 8 Find the general form of the equation of the circle
(x − 7)2 + (y + 2)2 = 9.
List the center and the radius of the circle. Graph the circle. Label the center and at
least one point on the circle.
Section 3.1 & 6.1
Question 9 Determine whether each relation is a function. For each function, state
the domain and range.
(a) {(−2, 2), (−1, −2), (0, 0), (2, 2), (0, 2)}
(b) {(−3, 1), (−1, 4), (1, −4), (3, 1)}
Question 10 Let g(x) =
3x
.
x2 −1
Show all work for each part.
1. Find g(−2).
2. Find g(−x).
3. Find −g(x).
4. Find g(x + 1).
Question 11 Find the domain of the function g(x) =
√
4 − 5x.
Question 12 Given f (x) =
3x+4
7x−9
and g(x) =
5x
.
7x−9
(a) Find (f + g)(x). What is the domain?
(b) Find (f − g)(x). What is the domain?
(c) Find (f · g)(x). What is the domain?
(d) Find ( fg )(x). What is the domain?
Question 13 The function F described by F (C) = 95 C + 32 gives the Fahrenheit temperature corresponding to the Celsius temperature C. Find the Fahrenheit temperature
equivalent to −25◦ C.
Section 3.2
Question 14 Determine whether each graph is a function by using the vertical line
test. If it is, use the graph to find:
(a) The domain and range
(b) The intercepts, if any
(c) Any symmetry with respect to the x-axis, the y-axis, or the origin
1.
2.
Question 15 Answer the following questions about the function g(x) =
a Is the point (1, 34 ) on the graph of g?
b If x = 3, what is g(x)? What point is on the graph?
c If g(x) = 1, what is x? What point(s) are on the graph of g?
d What is the domain of g?
e List the x-intercepts, if any, of the graph of g?
f List the y-intercepts, if any, of the graph of g?
x2 −2
.
x+3
Question 16 Answer the following questions using the given graph.
(a) Find f (−6), f (−1), and f (2).
(b) What is the domain of f ?
(c) What is the range of f ?
(d) List the intercepts of the graph of g?
(e) On what interval(s) is f (x) > 0?
(f ) How many times does the line y = 3 intersect the graph of f ?
(g) On what interval(s) is the graph constant?
(h) On what interval(s) is the graph increasing?
(i) On what interval(s) is the graph decreasing?
Section 3.3
Question 17 The graph of a function is given. Use the graph to find:
(a) The domain and range
(b) The intervals on which it is increasing, decreasing, or constant
(c) Whether it is even, odd, or neither
1.
2.
3.
Question 18 Determine algebraically whether each function is even, odd, or neither.
(a) f (x) =
−x3
4x2 −3
(b) g(x) = −3x4 − x2
(c) h(x) = 7x3 − 6
Question 19 The graph of a function is given. Use the graph to find:
(a) The numbers, if any, at which f has a local maximum value. What are the local
maximum values?
(b) The numbers, if any, at which f has a local minimum value. What are the local
minimum values?
1.
2.
Question 20 For each graph of y = f (x), find the absolute maximum and the absolute
minimum, if they exist.
1.
2.
Section 3.4
Question 21 Given the function

 5,
−x + 2,
f (x) =
 1
x − 34 ,
3
(a) Find the domain of the function.
−6 ≤ x < −3
−3 ≤ x < 1
1≤x≤7
(c) Graph the function.
(b) Locate any intercepts.
(d) Based on the graph, find the range.
(e) Is f continuous on its domain?
Section 3.5
Question 22 Find the function that is FINALLY graphed after each of the following
transformations is applied to the graph of y = x3 in the order stated.
(1) Shift up 2 units
(2) Reflect about the x-axis
(3) Reflect about the y-axis
Question 23 Graph the function h(x) = 2|x − 1| using the techniques of shifting,
compression, stretching, and/or reflecting. Start with the graph of the basic function
and show all stages. Find the domain and the range of the function.