General Properties Natural Logarithms
Llogbl=0 1.1n1=cfw_J
2.logbb=1 2.1ne=1
3. logb if)" = x cfw_:5 Imm '_:_- 3. 111 e" = x
a.
4. blogbx = I 55:.- rrorlriiu E';-. 4. 8],. = x
The Product Rule
Let b,
Parent Graph
as reects over the
mUItIP'i _ '31- a trans right
trans left
Always passes through
Vertical asymptote est! reects over the
. divide by e trans up
Domain trans down
Range
Imu. Graph using t
1.2 Domain and Range Notes
Finding the Domain of a Function Defined by an Equation
We can write the domain and range in interval notation
Finding Domain and Range from Graphs
Finding Domains and Range
1.3 RATES OF CHANGE AND BEHAVIOR OF GRAPHS NOTES
Using a Graph to Determine Where a Function is Increasing, Decreasing, or Constant
Use a graphing calculator
Analyzing the Toolkit Functions for Increa
Practice Worksheet: Modeling with Exponentiale and Logs
l] The table shows the atomic number x and the melting point y (in degrees Celsius] for ve alkali metals.
illllllllIEIIIIEIIIIHIIHEEIII
HIM III 7.2.4 Ambiguous Case
,
1. For
,
2. For
. Find all
to the nearest degree.
possible
. Find
to the nearest degree.
all possible
C
C
7
15
17
26
16
A
B
A
,
3. For
all possible
D
. Find
to the neare
Law of Sines and Cosines Word Problems
1. Juan and Romella are standing at the seashore 10 miles apart. The
coastline is a straight line between them. Both can see the same ship in the
water. The angl
HIM III
EULERS NUMBER AND NATURAL LOGS WORKSHEET
1. Simplify:
a)
2
b) ( )4
2. Evaluate without using a calculator
a) eln 5
b) ln e2
f) ln 1e
g) ln1
2x
3x
e) e 1 5e
c) 2ln e
h) eln10
d) e5ln 2
i) e3
HIM III Chapter 5 Team Test
NO CALCULATORS
Simplify all answers
1. Solve each equation or system of equations and check your solutions.
a.
2x 5
b. y = (x 5)2 4
= 3x + 4
c.
y+x+3=x1
d. 32x 1 = 81x
e. 3
HIM III 7.2.4 Law of Sines: Ambiguous Case (SSA)
Possible Triangles in SSA Case:
Let A be the angle and a and b the sides we know
If A is OBTUSE there are TWO possibilities
If a > b then ONE triangle
THE EIGHT LEGENDARY STEPS IN GRAPHING RATIONAL FUNCTIONS
WHAT TO DO?
1. Factor but dont cancel and
find the domain.
2. Simplify. Use this simplified
result from this point on.
HOW TO DO IT?
Domain is
HIM III Chapter 5 Team Test
Is log(0.3) greater than or less than 0? Justify your answer.
Solve each equation or system of equations and check your solutions.
1.
2=2
4.
+5=y
7.
2.
=x+5
3.
= 3x + 4
5.
HIM III
Chapter 7 Team Quiz SHOW ALL WORK
1. A bridge is being designed to connect two towns (one at point A and the other at
point C) along the shores of Lake Toftee in Minnesota. Lavanne has the
res
Log and Exponential Quiz CALCULATORS OK
1. Write the equation of an exponential function of the form y = abx + k that passes through
each of the following pairs of points and has the given asymptote.
HIM III 5.1.1 and 5.1.2 Quiz
NO CALCULATORS
1. Graph y = 5(x 2) and its inverse on the same set of
axes. Label the graph and the inverse function with
their equations.
2. Look at the graph of a functi
Name:
Date:
Period:
Practice Worksheet: Graphing Exponential Functions
Without a calculator, match each function with its graph.
_1]
_2]
_3]
_4]
_5]
_6]
A.
B.
C.
D.
E.
F.
Graph without a calculator. L
HIM III 7.2.1
Law of Sines
Find the area of each triangle to the nearest tenth.
11) The distance between Towns A and B is 56 mi. The angle formed by the road between
Towns A and B and the road between
HIM 1st Semester Final Review
1) Sketch a graph of an equation that has a domain of 3 x < 2 and a
range of 4 < y 1.
2) Investigate the function y = x2 x + 6.
3) List the error(s) in the solution at ri
Log and Exponential Quiz NO CALCULATOR
1. Compute the value of each expression without using a calculator.
log(8) + log(125)
log25(125)
1
2
7log7(12)
log(25) log(20)
Read each question and select the