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MAC 1105 - College Algebra
Final Exam
3
128
J
Jonse 0
Ojed
Date:_
Name:
Show your work; an answer alone, even correct, will get no credit. An illegible
will not be graded, so write your work neatly.
Find the center and radius of the circle with the given equation: Write the equation in the standard fo
1) x2 + y2 -18% + 8y=-61
cen
rad
standard
Find functions f and g so that fog=H. Neither f nor g can be identity functions
2) H6c) = (5 - 2x3)
Express as a single logarithm.
3) log3 (5x+2) – 2 log3 (x+5) – 4log3 (3x + 1)
:
7
3.42 + 3x
= 15
Find the distance d(P1, P2) between the points P1 and P2.
$) P1=(-1,-5); P2 = (6,-6)
Find the intercepts for the graph of the equation.
1
6
x-intercepts
y-intercepts
granh of a one to ono uno
the intercepts for the graph of the equation.
1
x2 - y2 + 5x + 6
y-intercepts
x-intercepts
The graph of a one-to-one function is given. Draw the graph of the inverse function f-1. For conveni
10
also given.
4-
(4.4)
3
2
+ +
st
2
5
6 x
1
U
-5
-6
-3
no
-2
-1
-4
(-1, -1)
3
Graph the function f by starting with the graph of y = x3 and using transformations (shifting, comp
reflection). Show the steps in the order a,b,c,d (see graphs) and write the formula for each function.
11) f(x) = - (x+1)3 + 1
y=
(a) y=x3
(b)
Iy
8
8
+
-6
4
را •
?
6
x
-6
-2
· --
. -6
- 8
(c)
y =
(d)
y = -(x+1)3 + 1
ca
S
6
T.
+
2
6
X
-6
T.
Graph the function using ita varten, avio of symmetry, and intercepto, Show Sun WHO)
12) k) =
-6
2
2
2
2
vertex:
Axis of symmetry:
x-intercepts:
y-intercept
Find the domain of the given function. Write it in the interval notation.
X-3
13) h(x) =
VE
7-8
Function fis one-to-one. Find the inverse f-1.
6x
x-2
£-1()=
14) f(x) =
Sketch the graph of the function. State the domain, find the intercepts and give the equations of asymptote
***
15) f(x) =
у
10
8
6
+
-10
-6
-4
of the function. State the domain, find the intercepts and give the equations of asymptote
- 2x
·10
8
-10
-8
-6
-4
-?
.-6
x-intercepts:
y-intercep
asymptote(s)
horizontal asymptote:
transformations to graph the function. Start with the basic function and show all steps in the order a, b, c. W
each function. Write the equations of asymptotes, if any.
16) f(x) = log3 (x+2) + 1
b) y
a) y =
VO
67
6
2
+
-6
6
-6
-2
2
4.
• A
-2
4
-6
--67
c) y = log3(x+2) + 1
>
6 х
-6
守
2
. -6
asymptote(s)
Graph the function.
17) **) - {**2 4 38*
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short answer for each Question
Exercise 13.1: Study of Patterns and Functions Apply your understanding of the learning from this chapter. When finished, ...
short answer for each Question
Exercise 13.1: Study of Patterns and Functions Apply your understanding of the learning from this chapter. When finished, submit your answers. Watch as this first-grade teacher introduces the ideas of a symbolic pattern. Lynda Penry 1st Grade: Using Symbols http://mediaplayer.pearsoncmg.com/assets/MM02_135_... What type of patterns are the children making in this video?How does the teacher engage the children to identify the core of the pattern?Near the end of the clip how does the teacher reinforce the learning of repeating patterns? "Repeating patterns are everywhere!" What happens in this lesson that demonstrates this to be true Exercise 15.1: Observing and Responding to Student Thinking Click the link below to watch a fifth-grade student solve the problem, "Use the ruler to illustrate the sums and differences" then answer the questions that follow. 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Sean, Decimal Assessment http://mediaplayer.pearsoncmg.com/assets/_video.true/imap-0375_iPad When the student in the video refers to the decimal point as the number behind a little dot, what concept is missing in his description?Based on this student's response what does he understand about decimal fraction place value?What would the next instructional step be to guide this student's thinking about comparing decimal fractions? Exercise 17.1: Observing and Responding to Student Thinking Click the link below to watch a sixth-grade student solve the problem, "Janet and Jeanette were walking to school, each walking at the same rate. Jeanette started first. When Jeanette has walked 6 blocks, Janet has walked 2 blocks. How far will Janet be when Jeanette is at 12 blocks?" Then answer the questions that follow. 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Identify and explain what they are for this scenario.The next step is selecting a random device for the key component. What would you recommend that they use for this activity?An important part of a simulation is determining and defining what constitutes "one trial." The authors recommend 10 times as one trial. Why is that appropriate for thissimulation? Exercise 22.1: Operations with Positive and Negative Numbers Apply your understanding of the learning from this chapter. When finished, submit your answers. Watch as this eighth-grade teacher "goes big" to guide her students' knowledge of working with larger integers. What's Your Sign: Integer Addition https://www.teachingchannel.org/video/adding-integers-lesson-idea What strategies is this teacher using to guide her students conceptual understanding of operations with integers?What concept does the color-coding help the students grasp?Why is the number line more effective in this lesson than using two color counters? 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8 pages
Answer 1 1
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