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MAC 1147 Exam #1
Name:
ID#
HONOR CODE: On my honor, I have neither given nor received any aid on this
examination.
Signature:
Instructions: Do all scratch work on the test itself. Make sure your final answers
are clearly labelled. Be sure to simplify all answers whenever possible. SHOW ALL
WORK ON THIS EXAM IN ORDER TO RECEIVE FULL CREDIT!!!
No.
1
2
3
4
5
6
7
8
Bonus
Total
Score
/10
/25
/10
/9
/12
/12
/12
/10
/10
/100
(1) For the function f defined by f (x) = 4x2 + 3x + 6, find the following values. Be
sure to simplify your answers as much as possible.
(a) f (−3) (3 points)
(b) f (−x) (3 points)
(c) f (x + h) (4 points)
(2) Use the graph of the function f below to answer the following questions.
(a) Find f (3). (1 point)
(b) Find f (−5). (1 point)
(c) Is f (1.5) positive or negative? (1 point)
(d) What is the domain of f ? (3 points)
(e) What is the range of f ? (3 points)
(f) For what numbers x is f (x) = 0? (5 points)
(g) Determine the intervals on which f is increasing and decreasing. Be sure to
specify which intervals are increasing and which are decreasing. (7 points)
(h) What are the local maxima? (2 points)
(i) What are the local minima? (2 points)
(3) Determine whether the function is even, odd, or neither.
(a) g(x) = x2 − 3x (4 points)
(b) f (x) =
x5
4x3 +2x
(4 points)
(c) The function graphed below. (2 points)
(4) Let f (x) be the piecewise defined function


2x + 1 if x < 0
f (x) = 2
if x = 0

 2
x
if 0 < x ≤ 2
(a) Find f (−2). (1 point)
(b) Find f (1). (1 point)
(c) Sketch the graph of f (x). (4 points)
(d) Find the domain and range of f (x). (3 points)
√
(5) Determine what transformations have been done to the function g(x) = x to
get the function f (x) below. Explain how you know. Then graph f (x). (12
points)
√
f (x) = −x − 1
(6) Determine what transformations have been done to the function g(x) = x3 to
get the function f (x) below. Explain how you know. Then graph f (x). (12
points)
f (x) = −(x + 3)3 + 2
(7) Determine what transformations have been done to the function g(x) = |x| to
get the function f (x) below. Explain how you know. Then graph f (x). (12
points)
f (x) = 3|x − 2| − 6
(8) Let f (x) be the quadratic function given below. Answer the following questions
about f (x). Justify all your answers.
f (x) = x2 − 4x
(a) Does the graph of f open up or down? How do you know? (1 point)
(b) What is the vertex (h, k) of f ? (1 point)
(c) What are the intercepts of f ? (2 points)
(d) What is the domain of f ? (1 point)
(e) What is the range of f ? (1 point)
(f) What are the intervals of increase and decrease of f ? (2 points)
(g) What does the graph of f look like? (2 points)
Bonus. The graph of f is given below. Use the graph of f to graph the function
G(x) = − 21 f (−x) + 3. (10 points)
Extra Blank Graphs.