Welcome to the Webinar

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Welcome to the WebinarLive Review for Test 1
(MAC 1105)
We will start promptly at 800 pm Everyone will
be placed on mute I am happy that you are able
to join us ?
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Note
The following slides present sample problems
similar to the test content, including the
worked-out solutions. These are a few problems
and do not include all the competencies tested on
Test 1. To be prepared for the test, you must
review the material from all the assigned
Chapters 1 and 2 sections and follow the Study
Guide posted on Blackboard!
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Find the x-and-y-intercepts of the graph of -3x
¾ y 18   To find the x-intercept, set y 0
-3x ¾ (0) 18 -3x 18
x -6 or (-6, 0) If asked for ordered
pair form, write your answer in the form (x, y).
If not asked for ordered pair form, then just
write the values as specified on the question.
To find the y-intercept, set x 0 -3(0) ¾ y
18 ¾ y 18 (4/3)(¾) y 18(4/3)
y 24 or (0, 24)
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• Slopes of Lines

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• Choose the graph that matches y ? x 5
• b.
• c. d.

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• Graphing y ? x 5 using the slope-intercept
  method
• First, identify the y-intercept and the slope
• (Remember y mx b, where m is slope and b is
  y-intercept)
• y-intercept is -5 or (0, -5)
• slope is ?
• Now, plot the y-intercept and from there, apply
  rise over run

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• Choose the graph that matches y ? x 5
• b.
• c. d.
• y-intercept is (0, -5). So, eliminate a and d.
• slope is 1/5. So, rise 1, run 5.
• Answer is b

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• What can we say about the slopes of the following
  lines?
• l4 is negative
• l1 , l2 are positive
• l3 is undefined
• l3 is zero
• Answer d

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Write the slope-intercept form of the equation
for the line passing through the points (-7, 6)
and (1, -3). First, find slope Use the
point-slope formula (with any of the given
points), and simplify to slope-intercept form
y y1 m(x x1)
y (-3) -(9/8)(x
1) y 3
-(9/8)(x 1)
y -(9/8)x (9/8) 3  
y -(9/8)x (9/8) (24/8)
y
-(9/8)x 15/8
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Parallel lines have negative reciprocal
slopes. a. True b. False
Your time to work! Poll Question
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Parallel lines have negative reciprocal
slopes. a. True b. False Answer
False Parallel lines have equal
slopes. Perpendicular lines have negative
reciprocal slopes.
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• True or False
• The equation of the line that passes through the
  point (1, 4)
• and is perpendicular to y -2x 6 is y -½
  x 9/2.
• Slopes are -2 and - ½, which are not negative
  reciprocals of
• each other!
• Answer False

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Find the point-slope form of the equation of the
line through the point (-2, 3) parallel to the
line 6x 3y 9 0. ?
First, change to slope-intercept form
by isolating the y 3y -6x 9 y -2x
3 Now, find a line with slope m -2 and
passing through (-2, 3). y
y1 m(x x1)
y 3 -2x (-2) y 3 -2(x 2)
You have to stop here! (asked
for point-slope form)
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• The line whose equation is y -6 has slope m
• -6
• -1/6
• 0
• 6
• Undefined
•  
• Your time to work!
• Poll Question

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• The line whose equation is y -6 has slope m
• -6
• -1/6
• 0
• 6
• Undefined
• Vertical Line x ?
• Horizontal Line y ?
• Answer c
• y -6 is a horizontal line, therefore, m 0

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True or False The following table represents a
function.   Function For each input, there
exists only one unique output Answer
True Different inputs can share the same output,
like (-3, 0) and (12, 0)
p -5 -3 6 7 12
q -1 0 7 -2 0
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• True or False The following graph represents a
  function.
• Passes Vertical Line Test?
• Yes.
• Answer True

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• For the following graph,
• Find C(150) b. Find x if
  C(x) 10
• C(150) means given the input of 150, find the
  output.
• Therefore, C(150) 20
• If C(x) 10, we are looking for x values where
  the output is10.
• Therefore, x 50 300

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• For the following function,
• Find domain and range
• Find increasing and decreasing intervals
• Domain (Input) 0 ? x ? 300 or 0, 300
• Range (Output) 5 ? y ? 25 or 5,
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• Increasing (0, 200)
• Decreasing (200, 300)

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Find the domain and range of the function f(x)
Domain Possible values of the input. Range
Possible values of the output. Domain or
2x 6 ? 0 2x ? 6 x ? 3 or 3,
infinity) Range y ? 0 or 0, infinity)

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• If p is the function f of q, then
• p f(q)
• the point (q, p) is on the graph of f
• f(0) p is the vertical intercept of f for
  some p value
• f(q) 0 is the horizontal intercept for some q
  value(s)
• the domain of f are all the possible values of
  q
• the range of f are all output values p
• all of the above
• h. none of the above
•  
• Your time to work!
• Poll Question

Answer using the Questions Box
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• If p is the function f of q, then
• p f(q)
• the point (q, p) is on the graph of f
• f(0) p is the vertical intercept of f for
  some p value
• f(q) 0 is the horizontal intercept for some q
  value(s)
• the domain of f are all the possible values of
  q
• the range of f are all output values p
• all of the above
• h. none of the above
•  
• Answer g

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• Dance Rooms Here charges 65 per hour and a 350
  deposit.
• a. Find a linear function that models this
  situation. Use C for cost
• and h for hours.
• b. Find and interpret the slope and the vertical
  intercept.
• c. If the total cost was 740, how many hours was
  the dance
• room used?
• d. Find and interpret C(4.5)
• a. Cost deposit fee plus rate per hour for
  each hour of use
• C(h) 350 65h
• Note
• This problem involves variables C and h. Using
  other variables not stated on
• the problem would be marked incorrect. Example,
  C(x) 350 65x.
• Make sure to use the variables as specified on
  each of the test questions!
• b. Slope 65. The cost increases at a rate of
  65 per hour.
• The vertical intercept is 350 and it denotes
  the initial fee.

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• c. If the total cost was 740, how many hours was
  the dance
• room used?
• d. Find and interpret C(4.5)
• c. We know C(h) 350 65h
• 350 65h 740 Solving for h we have
• 350 350 65h 740 350
• 65h 390
• 65h 390
• 65 65
• h 6 hours
• C(h) 350 65h
• C(4.5) 350 65(4.5)
• 350 292.5
• 642.5
• If the dance room is used for 4.5 hours,
  the cost is 642.50

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A test has 26 questions worth 100 points. The
test consists of multiple choice questions worth
2 points each and free response questions worth 6
points each. How many multiple choice questions
are on the test? First, establish a system of
equations. Let x multiple choice questions and
y free response questions Number of questions
x y 26 Question value 2x 6y
100 Multiply the first equation by -2, to help
us eliminate the x-terms (-2)(x y)
(26)(-2) So, we have -2x 2y -52 2x 6y
100 4y 48 y
12 Back-substitute y 12 into one of the
original equations to find x. x (12) 26 x
14 multiple choice questions
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If f(x) -x3 3x 5, find f(-2)
f(-2) -(-2)3 3(-2) 5 -(-8)
6 5 8 6 5
-3 So, f(-2) -3 that is, when the
input is -2, the output is -3.
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• If f(x) x2 2x h, find f(x h)
• f(x h) (x h)2 2(x h) h
• Note (x h)2 (x h) (x h) x² 2xh h²
• Therefore,
• f(x h) (x h)2 2(x h) h
• x² 2xh h² 2x 2h
  h
• x² 2xh h² 2x 3h

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Professor Vivaldi asked the students to evaluate
f(x h) given the function f(x) 3x2
6. Brendas answer 3x2 3h2 6 Mirandas
answer 3x2 6xh 3h2 6 T.J.s answer
6x2h2 6xh 6 Who is correct? a. Brenda b.
Miranda c. T.J. d. Neither
Your time to work! Answer using the Questions Box
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Professor Vivaldi asked the students to evaluate
f(x h) given the function f(x) 3x2 6. b.
Mirandas answer 3x2 6xh 3h2 6 f(x h)
3(x h)2 6 3(x2 2xh h2)
6 3x2 6xh 3h2
6
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• A group of friends can spend no more than 50 for
  popcorn and sodas at a concert. A small bag of
  popcorn costs 6 and a medium soda is 5. Let x
  represent popcorn and y represent a soda. Which
  of the following describes this scenario?
• 5x 6y ? 50
• 6x 5y ? 50
• 5x 6y ? 50
• 6x 5y ? 50
• x popcorn, 6 each ? 6x y soda, 5
  each ? 5y
• We can eliminate a and c.
• No more than 50 implies 50 dollars or less
• Answer is b.

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NOTE It is important that you follow the
instructions on the test. For example, if asked
for interval notation, write your answer using
interval notation. If you are not asked for
interval notation, then just write the values as
specified on the question. If asked for ordered
pair form, write your answer in the form (x, y).
If not asked for ordered pair form, then just
write the values as specified on the question.
So, read and follow instructions!
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This "live" review session has covered content
addressed on test 1, but you need to review
chapters 1-2 and complete all the problems
assigned on the study guide, so that you are
well-prepared for the test.
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Do well! ? gacosta_at_valenciacollege.edu