Vertical Line Test
A set of points.
A set of points where each
x-value has only one y-value.
If a relation is a function, a
vertical line will only cross
the function once at any point
on the graph.
(Anything you can sho
Applications of Exponents
Growth & Decay
The value of an antique vase increases by 10% every 7
years. If the vase was purchased for $200, approximately
how long will it take until it is worth $1000?
: 1000 (000:;00<l.l0
g: 200 5:0ljia
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= V ,_ QYI OOWUSV'
V0 9- XodV C)\law+ov|
Vo:a['% a) V0410 |
M 9 Vo-MDOO l
0 Ma 30
10 D [00 (aczi-ix +l2)1<a(x+3) Change ofBase
1. Evaluate each of the following:
VF b) logsl c) log212345 d) logiOYS
: WU = u? : 09 0'5-
Solving Trigonometric Equations Using Identities
Solve each of the following where 0 x 2. Use exact values where possible.
a) SinX + CosX = 0
b) 2Sin2X CosX 1 = 0
c) 2Tan2X + Sec2X 2 = 0
d) 2SecX = TanX + CotX
Solve each of the following
Final Exam Formula Sheet
b 2 - 4ac
A =A o (r)
pH = log[H+]
L =10 log
Sin2X + Cos2
Proving Trigonometric Identities Day 3
Prove each of the following:
Sin(X - p) =- SinX
Cos(X + Y)Cos(X Y) = Cos2XCos2Y Sin2XSin2Y
=CosX - SinX
Proving Trigonometric Identities Practice
Prove each of the following:
Determine the remainder when 6X2 + 5x - 2 is divided by x 3.
Remainder -= C0 '7
Remainder Theorem h *
I? 3614 Sub the \miue eat x. am makes time divisor*0
mm The dwudendJ our answer is He remaindf.
Find the remainder when:
1 Graphle following gIaphs on the same axis. Stale they-imam: horizonlal amptotgdomajn: range, and whemril is
inating-damning. Include a scale and at least 4 points on cad]. Show your tables.
_ , Base Transformed
Equatl an anon: X
Applications of Sinusoidal Functions
At the end of a dock, high tide is measured to be 14 m, and low tide is recorded 10 hours later at a
height of 6 m. A sinusoidal function can be used to model the depth of the water over time.
a) Graph three full tide
Sketching by Intercepts
Sketch the function y = 4x3 + 2x2 30x
Step #1: Factor
Step #2: Find YIntercept
Step #3: Find XIntercepts
Step #4: End Behaviour
Sketch the function y = (2x + 3)4(3x 1)5 + (2x + 3)3(3x 1)6
Power Functions & Transformations
Graph each of the following using a graphing calculator
and record a sketch in the space provided
y = x3
y = x3 + 2
y = x3 2
y = (x + 2)3
y = (x 2)3
y = (2x)3
y = ( 2 x)3
Label/Highlight each of following on the graph below.
A] Local Maximum
B] Local Minimum
C] Absolute Maximum
D] Absolute Minimum
E] Critical Point
F] Inflection Point
G] Increasing Section of the Curve
H] Decreasing Section of
Odd & Even Functions
For each of the following functions, state the degree of the function, the sign of the leading coefficient,
the type of symmetry, and whether it is an odd or even function.
Functions Review Homework
Determine if each relation is a function. State the domain and range.
Draw a graph that matches each of the following domains and ranges:
Domain: cfw_x = 2, 6, 1, 0, -3 | x R
Range: cfw_y = -4, 5, 1, 3
Identifying Degree of a Polynomial Function
y = 4x3 2x + 7
y = x(x + 3)(x 2)(x 6)
y = (x 4)3(x2 + 1)5
Table of Values
A power function is a function with _.
f(x) = 3x5
Even Degree Power Functions
Type of Symmetry:
1. For each of the following functions state the type of function, domain, range, x-intercept(s),
y-intercept(s), end behaviour, type of symmetry, and whether it is an odd/even function