Chabot Mathematics
§1.2 Graphs
Of Functions
Bruce Mayer, PE
Licensed Electrical & Mechanical Engineer
BMayer@ChabotCollege.edu
Chabot College Mathematics
1
Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH15_Lec-02_Fa13_sec_1-2_Fcn_Graphs.pptx
Review §
1.1
 Any QUESTIONS About
• §1.1 → Introduction to Functions
 Any QUESTIONS About
HomeWork
• §1.1 → HW-01
Chabot College Mathematics
2
Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH15_Lec-02_Fa13_sec_1-2_Fcn_Graphs.pptx
§1.2 Learning Goals
 Review the rectangular coordinate
system
 Graph several functions
 Study intersections of graphs, the
vertical line test, and intercepts
 Sketch and use graphs of quadratic
functions in applications
Chabot College Mathematics
3
Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH15_Lec-02_Fa13_sec_1-2_Fcn_Graphs.pptx
Points and Ordered-Pairs
 To graph, or plot, points we use two
perpendicular number lines called axes.
The point at which the axes cross is
called the origin. Arrows on the axes
indicate the positive directions
 Consider the pair (2, 3). The numbers in
such a pair are called the CoOrdinates.
The first coordinate, x, in this case is 2
and the second, y, coordinate is 3.
Chabot College Mathematics
4
Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH15_Lec-02_Fa13_sec_1-2_Fcn_Graphs.pptx
Plot-Pt using Ordered Pair
 To plot the point
(2, 3) we start at
the origin, move
horizontally to the
2, move up
vertically 3 units,
and then make a
“dot”
(2, 3)
• x=2
• y=3
Chabot College Mathematics
5
Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH15_Lec-02_Fa13_sec_1-2_Fcn_Graphs.pptx
Example  Plot the point (–4,3)
4 units left
3 units up
 Starting at the origin,
we move 4 units in
the negative
horizontal direction.
The second number,
3, is positive, so we
move 3 units in the
positive vertical
direction (up)
• x = –4;y = 3
Chabot College Mathematics
6
Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH15_Lec-02_Fa13_sec_1-2_Fcn_Graphs.pptx
Example  Read XY-Plot
 Find the coordinates of pts A, B, C, D, E, F, G
• Solution: Point A is 5 units
to the right of the origin and
3 units above the origin. Its
coordinates are (5, 3). The
other coordinates are as
follows:
–
–
–
–
–
–
B:
C:
D:
E:
F:
G:
(−2,4)
(−3,−4)
(3,−2)
(2, 3)
(−3,0)
(0, 2)
Chabot College Mathematics
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B
A
E
G
F
D
C
Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH15_Lec-02_Fa13_sec_1-2_Fcn_Graphs.pptx
Tool For XY Graphing
 Called “ Engineering
Computation Pad”
Graph on
this side!
• Light Green
Backgound
• Tremendous Help with
Graphing and
Sketching
• Available in Chabot
College Book Store
• I use it for ALL my
Hand-Work
Chabot College Mathematics
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH15_Lec-02_Fa13_sec_1-2_Fcn_Graphs.pptx
XY Quadrants
 The horizontal
and vertical
axes divide
the plotting
plane into
four regions,
or quadrants
(Abscissa)
(Ordinate)
• Note the
Ordinate &
Abscissa
Chabot College Mathematics
9
Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH15_Lec-02_Fa13_sec_1-2_Fcn_Graphs.pptx
The Distance Formula
 The distance between
the points (x1, y1) and
(x2, y1) on a horizontal
line is |x2 – x1|.
y
6
5
4
(5,4)
3
dV   4  4  8
2
1
x
0
 Similarly, the distance
between the points (x2,
y1) and (x2, y2) on a
vertical line is |y2 – y1|.
O
-1
-2
(-4,-2)
(3,-2)
d H  3   4  7
-3
-4
(5,-4)
-5
-6
-6
Chabot College Mathematics
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-5
-4
-3
-2
-1
0
1
2
3
4
5
6
XYGraph6x6HnVdistance.fig
Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH15_Lec-02_Fa13_sec_1-2_Fcn_Graphs.pptx
Pythagorean Distance
 Now consider any
two points (x1, y1)
and (x2, y2).
 These points,
along with (x2, y1),
describe a right
triangle. The
lengths of the legs
are |x2 – x1| and |y2 – y1|.
Chabot College Mathematics
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH15_Lec-02_Fa13_sec_1-2_Fcn_Graphs.pptx
Pythagorean Distance
 Find d, the length of the
hypotenuse, by using the
Pythagorean theorem:
d2 = |x2 – x1|2 + |y2 – y1|2
 Since the square of a number is the
same as the square of its opposite, we
can replace the absolute-value signs
with parentheses:
d2 = (x2 – x1)2 + (y2 – y1)2
Chabot College Mathematics
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH15_Lec-02_Fa13_sec_1-2_Fcn_Graphs.pptx
Distance Formula Formally
 The distance d between any two
points (x1, y1) and (x2, y2) is given by
d 
x2  x1    y2  y1 
Chabot College Mathematics
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2
2
Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH15_Lec-02_Fa13_sec_1-2_Fcn_Graphs.pptx
Example  Find Distance
 Find Distance
Between Pt1 & Pt2
 Use Dist Formula
d
d
d
Pt-2
x2  x1    y2  y1 
2
2
 2   8  6   2
2
6  8
2
2
2
Pt-1
 36  48
d  100  10
Chabot College Mathematics
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH15_Lec-02_Fa13_sec_1-2_Fcn_Graphs.pptx
Graphing by Dot Connection
 “Connecting the Dots” ALWAYS works
for plotting any y = f(x) from an eqn
T-Table for
 The procedure
y  f x   5e
x
• Use Fcn Eqn to make
a “T-Table”
• Properly Construct and
Label Graph
• Plot Ordered-Pairs in T-Table
• Connect Dots with Straight
or Curved Lines
Chabot College Mathematics
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x
y
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
0.74
1.02
1.40
1.92
2.65
3.64
5.00
6.87
9.45
12.99
17.86
24.56
33.76
Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH15_Lec-02_Fa13_sec_1-2_Fcn_Graphs.pptx
Making Complete Plots


1.

2.

3.




 5.


Chabot College Mathematics
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4.
Arrows in
POSITIVE
Direction Only
Label x & y axes
on POSITIVE ends
Mark and label at
least one unit on
each axis
Use a ruler for
Axes &
Straight-Lines
Label significant
points or quantities
Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH15_Lec-02_Fa13_sec_1-2_Fcn_Graphs.pptx
Example  Graph f(x) = 2x2
 Solution:
Make T-Table and
Connect-Dots
x
y
(-2,8)
0
(0, 0)
1
2
(1, 2)
(2,8)
8
7
6
5
4
(x, y)
0
(-1,2 )
3
2
(1,2)
1
-5 -4 -3 -2 -1
1
2 3 4 5
-1
x
–1
2
(–1, 2)
2
8
(2, 8)
 x = 0 is Axis of Symm
–2
8
(–2, 8)
 (0,0) is Vertex
Chabot College Mathematics
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y
-2
(0, 0)
Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH15_Lec-02_Fa13_sec_1-2_Fcn_Graphs.pptx
Plot PieceWise Function: f(x) = |x|
 ReCalling the Absolute Value Definition
can State Function in PieceWise Form
 x
y  f x   
 x
x0
x0
 Make T-Table from Above Fcn Def
 Class Question: What will be the
SHAPE of the the Graph of this
Function?
Chabot College Mathematics
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH15_Lec-02_Fa13_sec_1-2_Fcn_Graphs.pptx
Example  Graph f(x) = |x|
 Make T-table
x
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
Chabot College Mathematics
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5
y = |x |
6
5
4
3
2
1
0
1
2
3
4
5
6
y
6
4
3
2
1
x
0
-6
-5
-4
-3
-2
-1
0
1
2
3
-1
-2
 Plot Points, and
Connect Dots
-3
-4
-5
file =XY_Plot_0211.xls
-6
Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH15_Lec-02_Fa13_sec_1-2_Fcn_Graphs.pptx
4
5
6
Graph Intersections
 How To Find Solutions to the Equality
of Functions?
• Graph Both Functions and Find
Intersections
– At Intersections x & y are the SAME for both
functions, and ANY point on the graph is a
“Solution” to Fcn
 Thus at Intersections BOTH Fcns are
Simultaneously Solved
Chabot College Mathematics
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH15_Lec-02_Fa13_sec_1-2_Fcn_Graphs.pptx
Graph InterSection Example
 Consider two Functions: f x  7 cos x f x  ln x  1
 Want to Find solution(s), xs, such that
f 1 xs   7 cosxs   ln xs  1  f 2 xs 
 Note that this Equation can NOT Solved
exactly; The solutions are irrational
Numbers
1
2
• Such “NonAlgebraic” Eqns are Called
“Transcendental”
 Find Solution by Graph Intersection(s)
Chabot College Mathematics
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH15_Lec-02_Fa13_sec_1-2_Fcn_Graphs.pptx
Graph InterSection Example
Chabot College Mathematics
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8
6
f 1(x) = 7cos(x) • f2(x) = ln(x+1)
 Plot Both
Functions on
Same Graph
 Find
Intersection(s)
 Read xs from
intersection
points
4
f2
2
0
-2
-4
f1
-6
-8
0
1
≈1.44
2
3
4
x
5
≈4.97
Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH15_Lec-02_Fa13_sec_1-2_Fcn_Graphs.pptx
6
7
8
≈7.54
MSExcel vs Transcendental
 The “Goal Seek”
Command in
MicroSoft Excel to
Find xs with greater
Accuracy
 Use Excel to Solve
the Transcendental
Equation
7 cos x  ln x  1
Chabot College Mathematics
23
 Collect Terms on
One Side, and use
“Goal Seek” to find x
that satisfies eqn
7 cos x  ln x  1  0
 For the Eqn Above
the solutions, xs, are
called the “zeros” or
“roots” of the
“zeroed” eqn
Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH15_Lec-02_Fa13_sec_1-2_Fcn_Graphs.pptx
MSExcel vs Transcendental
 Use The “Goal Seek” Command in
MicroSoft Excel to Find xs with greater
Accuracy
Chabot College Mathematics
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH15_Lec-02_Fa13_sec_1-2_Fcn_Graphs.pptx
Goal Seek (on Data Tab)
Chabot College Mathematics
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH15_Lec-02_Fa13_sec_1-2_Fcn_Graphs.pptx
Goal Seek Results (2 Roots)
Chabot College Mathematics
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH15_Lec-02_Fa13_sec_1-2_Fcn_Graphs.pptx
Zeros Graphed by MATLAB
8
>> u = linspace(0, 2.5*pi, 300);
>> v = cos_ln(u);
>> xZ = [0,8]; yZ = [0, 0];
>> plot(u,v, xZ,yZ, 'LineWidth',3),
grid, xlabel('u'), ylabel('v');
>> Z1 = fzero(cos_ln,2)
Z1 =
1.4429
>> Z2 = fzero(cos_ln,5)
Z2 =
4.9705
>> Z3 = fzero(cos_ln,8)
Z3 =
7.5425
6
4
2
v
0
-2
-4
-6
-8
-10
0
1
Chabot College Mathematics
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2
3
4
u
5
6
7
8
Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH15_Lec-02_Fa13_sec_1-2_Fcn_Graphs.pptx
Power Function  f(x) = Kxn
 In the Power Function “n” can be ANY
number, positive, negative, rational or
Irrational. Some Examples
6
5
0
4.5
-10
4
-20
3.5
-30
3
-40
5.5
M15PwrFcnGraphs_1306.m
4.5
1.7
f(x) = -2x
f(x) = 5x
f(x) = 3x
2/7
-ln9
5
2.5
2
-50
-60
4
1.5
-70
1
-80
0.5
-90
3.5
3
0
2
4
6
x
Chabot College Mathematics
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8
10
0
0
2
4
6
x
8
10
-100
0
2
4
6
8
x Mayer, PE
Bruce
BMayer@ChabotCollege.edu • MTH15_Lec-02_Fa13_sec_1-2_Fcn_Graphs.pptx
10
PolyNomial Function
 The General PolyNomial Function
px   a n x n  a n1 x n 1  a n2 x n 2    a 2 x 2  a1 x1  a 0 x 0
or
px   a n x n  a n1 x n 1  a n2 x n 2    a 2 x 2  a1 x  a 0
 Where
• n ≡ a positive integer constant
• ak ≡ any real number constant
 n (the largest exponent) is called the
DEGREE of the Polynomial
Chabot College Mathematics
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH15_Lec-02_Fa13_sec_1-2_Fcn_Graphs.pptx
PolyNomial Function
 The plot of p(x) is continuous and
crosses the X-axis no more than n-times
 Some Examples
800
40
3500
600
20
400
3000
M15PloyNomialFcnGraphs_1306.m
4000
0
-20
2000
1500
0
p(x) = -3x2 - 7x + 19
p(x) = -5x3 - 7x2 + 4x + 23
p(x) = 1.7x4 - 8x3 + 3x2 - 8x - 247
200
2500
-200
-400
1000
-40
-60
-80
-600
500
0
-500
-6 -5 -4 -3 -2 -1
-120
-1000
0
x
Chabot College Mathematics
30
-100
-800
1
2
3
4
5
6
-1200
-6 -5 -4 -3 -2 -1
0
x
1
2
3
4
5
6
-140
-6 -5 -4 -3 -2 -1
0
x
1
2
3
4
5
Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH15_Lec-02_Fa13_sec_1-2_Fcn_Graphs.pptx
6
Rational Function
 A rational function is
a function f that is a
quotient of two
polynomials, that is,
p( x)
f ( x) 
,
q( x)
 Where
• where p(x) and q(x) are polynomials and
where q(x) is not the zero polynomial.
• The domain of f consists of all
inputs x for which q(x) ≠ 0.
Chabot College Mathematics
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH15_Lec-02_Fa13_sec_1-2_Fcn_Graphs.pptx
Rational Fcn Examples
 Note the Asymptotic Behavior
25
25
10
20
20
8
15
15
6
10
10
4
5
5
2
0
0
0
-5
-5
-2
-10
-10
-4
-15
-15
-6
-20
-25
-6 -5 -4 -3 -2 -1
f x 
0
x
1
2
2x
x3
3
Chabot College Mathematics
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4
5
-20
6
-25
-6 -5 -4 -3 -2 -1
f ( x) 
0
x
1
2
2x  3
x2  4
3
4
5
6 x 4  3x 2  1
f ( x)  4
9 x  3x  2
-8
6
-10
-2
-1.5
-1
-0.5
0
x
0.5
Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH15_Lec-02_Fa13_sec_1-2_Fcn_Graphs.pptx
1
1.5
2
Graphing & Vertical-Line-Test
 Test a Reln-Graph
to see if the Relation
represents a Fcn
 If no VERTICAL
line intersects the
graph of a relation
at more than one
point, then the
graph is the graph
of a function.
Chabot College Mathematics
33
Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH15_Lec-02_Fa13_sec_1-2_Fcn_Graphs.pptx
Example  Vertical-Line-Test
 Use the Vertical
Line Test to
determine if the
graph represents
a function
 SOLUTION
• NOT a function as
the Graph Does not
pass the
vertical line test
Chabot College Mathematics
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH15_Lec-02_Fa13_sec_1-2_Fcn_Graphs.pptx
Example  Vertical-Line-Test
 Use the Vertical
Line Test to
determine if the
graph represents
a function
 SOLUTION
• NOT a function as
the Graph Does not
pass the
vertical line test
Chabot College Mathematics
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TRIPLE
Valued
Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH15_Lec-02_Fa13_sec_1-2_Fcn_Graphs.pptx
Example  Vertical-Line-Test
 Use the Vertical
Line Test to
determine if the
graph represents
a function
 SOLUTION
• IS a function as the
Graph Does pass
the vertical line test
Chabot College Mathematics
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SINGLE
SINGLE
Valued
Valued
Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH15_Lec-02_Fa13_sec_1-2_Fcn_Graphs.pptx
Example  Vertical-Line-Test
 Use the Vertical
Line Test to
determine if the
graph represents
a function
 SOLUTION
• IS a function as the
Graph Does pass
the vertical line test
Chabot College Mathematics
37
SINGLE
Valued
Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH15_Lec-02_Fa13_sec_1-2_Fcn_Graphs.pptx
Quadratic Functions
 All quadratic functions have graphs
similar to y = x2. Such curves are called
parabolas. They are U-shaped and
symmetric with respect to a vertical line
known as the parabola’s line of
symmetry or axis of symmetry.
 For the graph of f(x) = x2, the y-axis is
the axis of symmetry. The point (0, 0) is
known as the vertex of this parabola.
Chabot College Mathematics
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH15_Lec-02_Fa13_sec_1-2_Fcn_Graphs.pptx
The Vertex of a Parabola
 The FORMULA for
the vertex of a parabola given by
f(x) = ax2 + bx + c:
 b
 b 4ac  b 2 
 b  
  2a , f  2a   or   2a , 4a .
 



• The x-coordinate of the vertex is −b/(2a).
• The axis of symmetry is x = −b/(2a).
• The second coordinate of the vertex is most
commonly found by computing f(−b/[2a])
Chabot College Mathematics
39
Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH15_Lec-02_Fa13_sec_1-2_Fcn_Graphs.pptx
Graphing f(x) = ax2 + bx + c
1. The graph is a parabola.
Identify a, b, and c
2. Determine how the parabola opens
•
If a > 0, the parabola opens up.
•
If a < 0, the parabola opens down
3. Find the vertex (h, k). Use the formula
 b
 b 
h, k     , f    .
 2a
2a 
Chabot College Mathematics
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH15_Lec-02_Fa13_sec_1-2_Fcn_Graphs.pptx
Graphing f(x) = ax2 + bx + c
4. Find the x-intercepts
Let y = f(x) = 0. Find x by solving the
equation ax2 + bx + c = 0.
•
If the solutions are real numbers,
they are the x-intercepts.
•
If not, the parabola either lies
– above the x–axis when a > 0
– below the x–axis when a < 0
Chabot College Mathematics
41
Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH15_Lec-02_Fa13_sec_1-2_Fcn_Graphs.pptx
Graphing f(x) = ax2 + bx + c
5. Find the y-intercept. Let x = 0. The
result f(0) = c is the y-intercept.
6. The parabola is symmetric with
respect to its axis, x = −b/(2a)
•
Use this symmetry to find
additional points.
7. Draw a parabola through the points
found in Steps 3-6.
Chabot College Mathematics
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH15_Lec-02_Fa13_sec_1-2_Fcn_Graphs.pptx
Example  Graph
f x   2x 2  8x  5.
 SOLUTION
Step 1 a = –2, b = 8, and c = –5
Step 2 a = –2, a < 0, the parabola opens down.
Step 3 Find (h, k).
b
8
h

2
2a
2 2 
k  f 2   2 2   8 2   5  3
2
h, k   2, 3
Maximum value of y = 3 at x = 2
Chabot College Mathematics
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH15_Lec-02_Fa13_sec_1-2_Fcn_Graphs.pptx
Example  Graph
f x   2x 2  8x  5.
 SOLUTION
2
2x
 8x  5  0
Step 4 Let f (x) = 0.
x
8 
8 
2
 4 2 5 
2 2 
4 6

2
4 6
4 6
x-intercepts are
and
.
2
2
Step 5
Let x = 0. f 0   2 0   8 0   5
y-intercept is  5 .
Chabot College Mathematics
44
2
Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH15_Lec-02_Fa13_sec_1-2_Fcn_Graphs.pptx
Example  Graph
f x   2x 2  8x  5.
 SOLUTION
Step 6 Axis of symmetry is x = 2. Let x = 1,
then the point (1, 1) is on the graph, the
symmetric image of (1, 1) with respect to
the axis x = 2 is (3, 1). The symmetric
image of the y–intercept (0, –5) with
respect to the axis x = 2 is (4, –5).
Step 7 The parabola passing through the points
found in Steps 3–6 is sketched on the
next slide.
Chabot College Mathematics
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH15_Lec-02_Fa13_sec_1-2_Fcn_Graphs.pptx
Example  Graph
f x   2x 2  8x  5.
 SOLUTION cont.
• Sketch Graph
Using the points
Just Determined
f x   2x  8x  5
2
Chabot College Mathematics
46
Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH15_Lec-02_Fa13_sec_1-2_Fcn_Graphs.pptx
WhiteBoard Work
 Problems §1.2-44
• Supply & Demand
Chabot College Mathematics
47
Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH15_Lec-02_Fa13_sec_1-2_Fcn_Graphs.pptx
All Done for Today
AutoMobile
Stopping
Distance
Chabot College Mathematics
48
Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH15_Lec-02_Fa13_sec_1-2_Fcn_Graphs.pptx
Chabot Mathematics
Appendix
r  s  r  s r  s 
2
2
Bruce Mayer, PE
Licensed Electrical & Mechanical Engineer
BMayer@ChabotCollege.edu
–
Chabot College Mathematics
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH15_Lec-02_Fa13_sec_1-2_Fcn_Graphs.pptx
Chabot College Mathematics
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH15_Lec-02_Fa13_sec_1-2_Fcn_Graphs.pptx
Chabot College Mathematics
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH15_Lec-02_Fa13_sec_1-2_Fcn_Graphs.pptx
Chabot College Mathematics
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH15_Lec-02_Fa13_sec_1-2_Fcn_Graphs.pptx
(120, 0)
Chabot College Mathematics
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH15_Lec-02_Fa13_sec_1-2_Fcn_Graphs.pptx
Chabot College Mathematics
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH15_Lec-02_Fa13_sec_1-2_Fcn_Graphs.pptx
Chabot College Mathematics
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH15_Lec-02_Fa13_sec_1-2_Fcn_Graphs.pptx
Chabot College Mathematics
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH15_Lec-02_Fa13_sec_1-2_Fcn_Graphs.pptx
MTH15 P1.2-44 • Bruce Mayer, PE
800
Graph by MATLAB
700
E ($k/Month)
600
500
400
300
200
100
0
M15P12441306.m
0
20
40
60
80
100
120
p ($/Unit)
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH15_Lec-02_Fa13_sec_1-2_Fcn_Graphs.pptx
MATLAB Code
% Bruce Mayer, PE
% MTH-15 • 23Jun13
% M15P12441306.m
%
% The FUNCTION
p = linspace(0,120,500); E = -p.^2/5 + 24*p;
%
% the Plot
axes; set(gca,'FontSize',12);
whitebg([0.8 1 1]); % Chg Plot BackGround to Blue-Green
plot(p,E, 'LineWidth', 3),axis([0 120 0 800]),...
grid, xlabel('\fontsize{14}p ($/Unit)'),
ylabel('\fontsize{14}E ($k/Month)'),...
title(['\fontsize{16}MTH15 P1.2-44 • Bruce Mayer,
PE',]),...
annotation('textbox',[.55 .055 .0 .1], 'FitBoxToText',
'on', 'EdgeColor', 'none', 'String',
'M15P12441306.m','FontSize',9)
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH15_Lec-02_Fa13_sec_1-2_Fcn_Graphs.pptx