Application of Matrix Multiplication Assignment
The scenario:
1*
Two factories, one in Austin, one in San Antonio
2*
Each manufactures two kinds of skis: trick and
slalom
3*
Two manufacturing steps: fabricate and finish
4*
Per-hour labor costs differ by s
Question 7
0 out of 5 points
Find f-1(x)
f(x) = 3x + 15
Selected Answer:
D.
f-1(x) = x 5
Correct Answer:
A.
f (x) = (x 15)/3
-1
Question 8
5 out of 5 points
Find f 1(x).
f(x) = x 9
Selected Answer:
f 1(x) = x + 9
Correct Answer:
f 1(x) = x + 9
Question
You've been playing with "y =" sorts of equations for some time now. And
you've seen that the "nice" equations (straight lines, say, rather than
ellipses) are the ones that you can solve for "y =" and then plug into your
graphing calculator. These "y =" e
How do we go about evaluating functions? First, remember this: While
parentheses have, up until now, always indicated multiplication, the
parentheses do not indicate multiplication in function notation. The
expression "f(x)" means "plug a value for x int
1
2.5 out of 2.5 points
Perform the operation:
(2 + 3i) + (5 6i)
Selected
Answer:
Correct
Answer:
A.
73i
A.
73i
Question 2
0 out of 2.5 points
Perform the operation:
(5 i) (4 + 8i)
Selected
Answer:
Correct
Answer:
D.
9
+ 9i
B.
99i
Question 3
2.5 out of 2.
Question 1
5 out of 5 points
Use the vertical line test to determine if the following graph is the graph of
a function.
Selected
Answer:
Correct
Answer:
A.
not a
function
A.
not a
function
Question 2
10 out of 10 points
The Domain of the function f(x) = [
Use the quadratic formula to solve the following quadratic equation. Check
your solutions by using the sum and product relationships.
5n 2 31n = 0
Selected
Answer:
Correct
Answer:
Question 2
5 out of 5 points
Write
in terms of i and simplify.
Selected
An
Question 1
5 out of 5 points
6x + 1
Solve the Exponential Equation: 7
Selected
Answer:
Correct
Answer:
= 49
C.
x=
1/6
C.
x=
1/6
Question 2
5 out of 5 points
2x 7
Solve the Exponential Equation: 3
Selected
Answer:
Correct
Answer:
= 27
D.
x
=5
D.
x
=5
Quest
Question 1
5 out of 5 points
Determine the position of the vertex, the opening and the equation or the axis of
symmetry for the grapf of the Quadratic Function:
f(x) = 3( x - 1)2 - 5
Selected
Answer:
B.
parabola opens up
vertex: (1, -5) ; axis of
symmetry
Question 1
5 out of 5 points
Match the graph with the Rational Function
Selected
Answer:
A.
Correct
Answer:
A.
Question 2
5 out of 5 points
Use the Horizontal Line Test to determine which of the following functions
graphed below has an inverse function
Se
Question 2
5 out of 5 points
Let f(x) = -5x2 - 3x +1, evaluate f(-1)
Selected Answer:
C.
-1
Correct Answer:
C.
-1
Question 3
5 out of 5 points
Let f(x) = 2x2 - 4x, evaluate f(2)
Selected Answer:
B.
0
Correct Answer:
B.
0
Question 4
5 out of 5 points
Th
Question 1
5 out of 5 points
Determine the position of the vertex, the opening and the equation or the axis of symmetry
for the grapf of the Quadratic Function:
f(x) = x2 + 8
Selected Answer:
A.
parabola opens up
vertex: (0, 8) ; axis of symmetry: x = 0
Combining Functions - Part II
What good is functional composition?
Suppose the Cost of producing x units in a manufacturing
process is given by the function C:
C(x) = 60x + 750
The Number of units produced in t hours is given by function N:
N(t) = 50t
Wha
Properties of Logarithms Notes
Can you do this in your head? 100 x 1000 = ?
Recall: if m = 102 then 2 = log m *
100000
mn
=
=
100
m
x 1000
x n
105
10log mn
10log mn
=
=
=
102 x 103
10log m x 10log n (by *)
10log m + log n (laws of exponents)
log mn = log
Properties of Matrices Notes
A matrix is a rectangular array of numbers.
The anatomy of a matrix
each element
col
col
has a name:
2
3
a12
a13
3
5
a
1
= 11
2
a
a 22
a 23
1
3
21
col
1
row 1
row 2
row dimension: 2
column dimension: 3
dimension of mat
Piecewise-defined Functions Notes
Definition: A function defined symbolically (using a
formula), but using a different formula for different parts of
its domain.
Example:
f(x) = 2
-2
if x < 0
if x 0
So, f(-1) = 2, f(2) = -2, f(0) = ?
f(100) = ?
Heres the
Logarithmic Functions and Models
y = log (x)
(read: "log of x")
Log is a function (the common logarithm) defined by:
y = log(x)
means
10y = x
Example: Since 103 = 1000, then 3 = log(1000)
The common log of a number is that exponent to which
10 must be rai
Inverses of Matrices Notes
We know that
1 a = a 1 = a (for all real numbers
a)
Multiplying any number by 1 yields the identical
number
1 is called the multiplicative identity element for the
real number system
Now note:
a
c
b 1
d 0
0 1
1 0
0 a
1 c
b
Combining Functions Notes
Two functions:
x
f(x)
g(x)
1
2
3
2
6
0
3
4
-1
New function, which we call f + g:
x
(f+g)(x)
1
5
2
6
3
3
Inputs (domain) f + g:
Outputs:
Definition:
same as f and g
add outputs of f and g
(f + g)(x) = f(x) + g(x)
(f - g)(x) = f(
Formal definition of the inverse function f-1
If:
f(g(x) = x for all x in the domain of g, and
g(f(x) = x for all x in the domain of f
Then:
g is the inverse function for f (g = f-1)
Inverses of functions represented as (mapping) diagrams
to get f-1 , swi
Inverse Functions and their Representations
Inverses of functions represented numerically (by table)
x
f(x)
0
5
5
10
10
15
15
20
Lets play a perverse game with f (input-output game
backwards).
The perverse function we just demonstrated
Is called the inv
Exponential and logarithmic equations
How to solve exponential equations
(1) get equation into form:
a(expression with x in it) = (expression without x)
(2) take log or ln of both sides
(3) apply inverse property:
loga ax = x
or log of a power property: l
Question 1
5 out of 5 points
Solve the Exponential Equation: 102x 3 = 1000
Selected Answer:
D.
x=3
Correct Answer:
D.
x=3
Question 2
5 out of 5 points
Solve the Exponential Equation: 53x 9 = 125
Selected Answer:
A.
x=4
Correct Answer:
A.
x=4
Question 3