CMR/TRIG FINAL EXAM REVIEW
Exponential Functions
f (x) = 3x
x
-3
-2
-1
0
1
2
3
Does this graph exhibit exponential growth or decay? _______________.
x
⎛ 1 ⎞x
f (x) = ⎜ ⎟ + 1
⎝ 3⎠
-3
-2
-1
0
1
2
3
Asymptote:
Domain:
Range:
y-intercept
Parent Function
Translation of Parent Function
Does this graph exhibit exponential growth or decay? _______________.
CMR/TRIG FINAL EXAM REVIEW
Exponential Regression
a.) Graph a scatterplot of the data in your graphing calculator.
b.) What type model is best to model this situation?
c.) Base on the new equation, what was the initial temperature of the
coffee?
d.) When is the coffee at a temperature of 106 degrees?
e.) What is the predicted temperature of the coffee after 1 hour?
CMR/TRIG FINAL EXAM REVIEW
a.) Write the exponential decay model for the data.
b.) Based on your above model, find the remaining grams of DDT at
the end of 15 years.
a.) Write the exponential growth model for the data.
b.) Based on your above model, find the amount of bacteria after 26
hours.
CMR/TRIG FINAL EXAM REVIEW
Logarithmic Functions
Evaluate the following logarithms.
a.) log 6 1
c.) log 9 81
c.) log 8
1
64
y = log 3 x
b.) log 4
1
4
d.) log10
1
100
1
log
1
e.)
49
7
y = log 3 (x −1) − 3
CMR/TRIG FINAL EXAM REVIEW
f (x) = log 2 x
f −1 (x) = ____________
Special Right Triangles
Find the value of each variable using the rules of special right triangles.
Write answers in simplest radical form.
.
x =____ y = _____
x =____ y = _____
x =____ y = _____
CMR/TRIG FINAL EXAM REVIEW
SOHCAHTOA
Coterminal Angles
Find and plot one positive and one negative angle that are coterminal with
the following angles:
a.) -320°
b.) 125°
Positive :_____________
Positive: ________
Negative: ____________
Negative: _______
CMR/TRIG FINAL EXAM REVIEW
Converting Between Degrees and Radians
92° = __________ radians
13π
radians = _________ degrees
6
Arc Length
θ = 119.7°
r = 5.49 mm
s = ________
Evaluating Tirg Functions Given a Point
If (2,-1) is a point of the terminal side of an angle
evaluate the six trigonometric functions of θ .
θ
sin θ =
csc θ =
cos θ =
sec θ =
tan θ =
cot θ =
in standard position,
Exact Values of Trig Functions
Use reference angles to evaluate the following trigonometric functions
a.) tan (135°)
b.) sin (-60°)
c.) cos (210°)
CMR/TRIG FINAL EXAM REVIEW
Graphing Trig Functions
⎛1 ⎞
y = 3 sin ⎜ x ⎟
⎝2 ⎠
Interval:
-360 ≤ x ≤ 720
Domain: _______________________
x-intercepts:_______________________
Range:_________________________
y-intercept:________
Amplitude: ____________________
Period: ________________________
y = 5 cos (3x)
Interval: -120 ≤ x ≤ 240
Domain: _______________________
x-intercepts:_______________________
Range:_________________________
y-intercept:________
Amplitude: ____________________
Period: ________________________
CMR/TRIG FINAL EXAM REVIEW
The table shows the average sales S (in millions of dollars) of an
outerwear manufacturer for each month t, where t = 1 represents
January.
Month, t Sales, S
1
13.46
2
11.15
3
8.00
4
4.85
5
2.54
6
1.70
7
2.54
8
4.85
9
8.00
10
11.15
11
13.46
12
14.30
a. Create a scatter plot of the data in your calculator.
b. Find a trigonometric equation that fits the data. Graph the
model on your scatter plot. How well does the model fit?
c. Based on the data, what is the period of the model?
What period is given by a calculator’s regression equation?
d. Interpret the meaning of the model’s amplitude in the problem
situation.
CMR/TRIG FINAL EXAM REVIEW
Logistic Functions
Graph y =
c = _____
4
1+ 2.5e−4 x
a = _____ r =_______
Asymptotes: _____________
Domain: ______________
Range:
___________
y-intercept: _____________
Maximum Growth Point: ___________
When did the deer population at the wild west animal preserve reach its
maximum growth rate?