Math 1111- Summer 2013
Score:
Name:
Test 2: Sections 2.4, 3.1-3.7
Directions: ONLY use PENCIL please. Work each of the problems out in the space provided, and show all of your work.
Leave all answers in reduced fraction form. Each problem is worth 4.4 points.
1. Find an equation of the line that satisfies the given conditions. Section 2.4
Through (1, −6); perpendicular to the line x + 2y = 6.
Use the equation, 4x – 3y = 12, in order to complete problems 2 – 4. Section 2.4
2. The slope of 4x – 3y = 12 is ___________.
3. The y-intercept of 4x – 3y = 12 is _______________. (Write your answer as an ordered pair.) (x, y)
4. Graph 4x – 3y = 12 below.
5. Evaluate f(x) = x3 + 3x2 – 5x for f(-2). Section 3.1
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Leave all answers in reduced fraction form.
𝑥𝑥 2 + 2𝑥𝑥
6. Evaluate 𝑓𝑓(𝑥𝑥) = �𝑥𝑥 − 5
𝑖𝑖𝑖𝑖 𝑥𝑥 < −2
𝑖𝑖𝑖𝑖 − 2 ≤ 𝑥𝑥 ≤ 2
5
𝑥𝑥
7. Find the difference quotient,
8. Find the domain of 𝑓𝑓(𝑥𝑥) =
𝑓𝑓(𝑎𝑎+ℎ)−𝑓𝑓(𝑎𝑎)
,
ℎ
1
.
2𝑥𝑥−5
9. Sketch the graph of 𝑓𝑓(𝑥𝑥) = �
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for f( 0). Section 3.1
𝑖𝑖𝑖𝑖 𝑥𝑥 > 2
for f(x) = x2 + 2. Section 3.1
Make sure to use interval notation. Section 3.1
−2𝑥𝑥
𝑥𝑥 + 5
𝑖𝑖𝑖𝑖 𝑥𝑥 < 0
. Section 3.2
𝑖𝑖𝑖𝑖 𝑥𝑥 ≥ 0
Leave all answers in reduced fraction form.
10. Use the vertical line test to determine if the curve is the graph of a function of x. Circle your answer. Section 3.2
Yes, it is a function.
No, it is not a function
11. Determine whether the equation defines y as a function of x. Show all of your work OR explain in complete
sentences why you selected your answer. Section 3.2
x + y2 = 9
Use the following graph, f(x) to answer questions 12 – 17. Section 3.3
12. Find f(-2)
13. Find the domain of f(x). Make sure to use interval notation.
14. Find the range of f(x). Make sure to use interval notation.
15. Find the value(s) of x for which f(x) < 0. Make sure to use interval
notation.
16. Determine the interval(s) on which the function is decreasing.
Make sure to use interval notation.
17. There is a local minimum of ________ when x is __________.
18. Suppose the graph of f is given. Describe how the graph of the following function can be obtained from the
graph of f. Circle your answer. Section 3.5
y = f(x – 4) + 3
A.
B.
C.
D.
E.
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Vertical shift down 4 units, horizontal shift right 3 units
Horizontal shift left 4 units, vertical shift up 3 units
Horizontal shift right 4 units, vertical shift up 3 units
Vertical shift up 4 units, horizontal shift left 3 units
Vertical shift down 4 units, horizontal shift left 3 units
Leave all answers in reduced fraction form.
19. Given the following graph of a function, determine the average rate of change of the function between the
indicated points on the graph. Section 3.4
20. Determine whether the function f is even (y-axis symmetry), odd (origin symmetry), or neither. Show all of your
work OR in complete sentences, describe why you selected your answer. Section 3.5
f(x) = x4 – 4x2
21. Given f(x) = x2 and g(x) = √𝑥𝑥 − 3, find 𝑓𝑓 ∘ 𝑔𝑔. Section 3.6
22. What is the domain of problem 21? Make sure to use interval notation. Section 3.6
23. Find the inverse of f(x) = 5 – 4x3. Section 3.7
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Leave all answers in reduced fraction form.