Grade 11 functions

Unit 1: Functions

100

What is the vertical line test?

When on a grid, the image only has one point at any given time passes through a vertical line.

200

What is the base equation for a rational function?

y=1/x

300

Simplify the radical expression

(√3 - 2√2) (√2 - √3)

=√6 - 3 - 2(2) - 2√6

= -√6 - 7

400

Rewrite the equation in vertex form

f(x)= 3x²+8x+2

f(x)= -2x²+8x-3

f(x)= -2(x²+4x)-3

f(x)=−2(x2−4x+4)+8−3 

f(x)=−2(x−2)2+5 

Vertex = (2,5)

500

Simplify

8√ 3+5√ 12-2√ 75

=8√ 3+5√ 4x3 - 2√ 25x3

=8√ 2+10√ 3 - 10√ 3

=8√2

Unit 2: rational expressions

100

simplify

18/4

9/2

200

Simplify

2/5 ÷ 1/4

= 2/5 x 4/1

=8/5

300

Simplify

6x-10

5-3x

= -2(-3x+5)

     5-3x

= -2

400

Describe the transformation

y = -3(x-7)²-6

Reflection in the x-axis

Vertical stretch by a factor of 3

Translate 7 units right and 6 units up

500

determine the equation in inverse

y=(x+8)²

x=(y+8)²

√x-8=y

Unit 3: Exponential Functions

100

Power of a power

(x^ay^b)^c

x^acy^bc

200

Simplify

(3a³b)²(2pq²)³

=(9p³q²)(8p³q⁶)

=72p⁹q⁸

300

What is a asymptote?

An invisible line that the function will never cross.

400

Solve

81^1/2

=9

500

Simplify

√√16m⁸

=(16m^8/2)^1/2

=16m^8/4

=2m²

Unit 4: Trigonometry

100

When given a right angle triangle, what do we use to find missing sides and angles?

SOH CAH TOA

200

Which of the following is a special angle of the unit circle?

A)210

B)200

C)190

D)342

A)210

300

What is the cosine law formula we use when trying to find a missing side?

a²=b²+c²-2bc cos(A)

400

When do you use sine law?

when we are given either a) two angles and one side, or b) two sides and a non-included angle.

500

Given that sin A=3/5 and that angle A lies in the first quadrant, determine the exact values of cos A and Tan A.

x²+3²=5²              CosA = 4/5

x=4                      TanA = 3/4 

Unit 5: Trigonometric Functions

100

Domain for any sine or cosine curve

{x∈R}

200

The maximum value of the function y = sin x - 6 is...

-5

300

Describe the transformations

y=6 sin [2(x+22)]+7

Vertical stretch by a factor of 6

Horizontal compression by a factor of 1/2

Phase shift 22° left

Translate 5 units up

400

A cosine function has a period of 45°, is reflected across the x axis, and has a amplitude of 4. Determine its equation.

y = -4 cos 8x

500

Verify the identity

cosθ²-sinθ² = 2cosθ²-1

LS                  RS

LS= cosθ²-sinθ²

=cosθ²-(1-cosθ²)

=cosθ²-(1+cosθ²)

=2cosθ²-1

LS=RS