Advanced Functions

Polynomial Functions

100

What are the two other names of a Zero of a function?

x-intercept and roots

200

What is the end behaviour of a graph that has a positive leading coefficient and odd degree?

3 -> 1

300

Determine the equation of the polynomial function with a root at -2, a double root at 5, and passes through the point (-1,4).

y= 1/9(x+2)(x-5)²

400

Does the following equation have Even, Odd, or Neither symmetry. 

f(x) = 4x² + 3 

Even

500

Describe the Following Transformations of the Polynomial Function. 

y = -3(2x+4)⁴ -6

-> Reflection on x-axis

-> Vertical stretch BAFO 3

-> Horizontal Compression BAFO 1/2

-> Shifted 4 units left

-> Shifted 6 units down

Polynomial Equations and Inequalities

100

By using The Remainder Theorem, 

Divide P(x) = 3x³ + 6x² + x - 2 by x + 2 to find the Remainder.

-4

200

Factor the following fully.

x³ + 2x² - 5x + 2

(x-1), x= -3+-(root)17/2

300

Solve the following Polynomial Equation

2x³ - x² -8x+ 4 = 0

   x= -1/2,2,-2

400

Solve the Linear Inequality 

2(3x + 1) > -4(6 - x) 

      x > -14

500

Solve the Polynomial Inequality 

-2x³ - 6x² + 12x + 16 _>_ 0 

x _<_-4, -1_<_ x _<_2

Rational Functions

100

Determine the x and y intercepts of the following.

y = x - 2/x + 3

y =   (0,-2/3)

x = (2,0)

200

Determine the Oblique Asymptote.

 y = x² + 3x - 5/ x + 2

 O:A y=x-6

300

Determine the Vertical and Horizontal Asymptotes of the following.

f(x) = 2x² - 5x/ x² - 1

V.A: x = 1, x = -1

H.A: y = 2

400

Solve the following Rational Equation.

x - 4/ x² + 2x - 3 = 2 + 3/ x - 1

x= -13/10

500

solve the Rational Inequality 

2/x - 4 < 8

x < 4, x > 4.2

Trigonometric Functions, Equations, and Identities

100

Change the following Radian into Degrees.

4pie/3

240 degrees

200

Solve the following Trigonometric Equation by collecting liked terms.

sinx + root 2 = - sinx

     x=5(pi)/4 , 7(pi)/4

300

Using the Compound Angle Formula determine the exact value of the following. 

Cos(pie/2 - pie/4)

= 1+(root)3/2(root)2

400

If cos x = -1/2 and is in quadrent 3, determine the value of cos 2x and sin 2x.

cos 2x = 1/2

sin 2x = (root)3/2

500

Prove the following Trig Identities.

cos 2x - 1/sin 2x = - tan x

    LS=RS

Logarithmic Functions

100

Change into Logarithmic form.

3⁵ = 243

Log₃243 = 5

200

Evaluate the Logarithm

Log₃ 405 + Log₃ 5

4

300

Solve the following Exponential Equation.

3^{x + 2} - 4 = 31

x = 1

400

Solve the following Logarithmic Equation. 

Log₃ x + Log₃ (x - 6) = 3

x= -3   

x= 9

500

On August 22 Canada received it's largest earthquake recorded at 8.1 on the richer scale. How many times more intense was the Canada earthquake than one with a magnitude of 6.6?

Ic= 31.6 Im