MCR3U Grade 11 Functions Math Functions Test

Required to study:

-Domain and Range
-Function Notation and evaluating function notation equations. i.e  f(x), f(3)
-Functions :

-Vertical Line Test

-Mapping Notation – one to one mapping

-Solving Quadratic Equations

-Factoring

-Quadratic Equation [-b+- root (b^2-4ac)] / [2a]

-Discriminant and number of roots

-Solving for max and min

-Partial Factoring -b/2a

-Completing the square into y=a(x-h)^2+k

1 Factor out so that a is equal to 1

2 If factored, only factor B term

3 Divide B term by 2, add b/2 inside squared and subtract outside

bracket squared

4 Factor x^2+(b/2)^2 into (x-(b/2)^2

5 Expand terms outside of bracket

6 Multiply -(b/a) on the outside with factored term in front if factored

7 Collect like terms and solve.

-averaging x-intercepts

Solving Radicals

-Treat Radicals like like term variables

-root 2 * root 4 = root (2*4)

-6 root 5 * 4 root 3 = 6*4 root (5*3) = 24 root 15

(root 5 + 1)x = root 5 + x

-(root 5 + 1) root x = root 5 x + root x

-Mixed Radicals i.e. Root 27 = root 9*3 = 3 root 3

-Families of quadratics

-y= a(x-s)(x-r)

-fractional x intercepts need to be reversed.

⅓ = x

1=3x

3x-1=0

Y=a(3x-1)(…

-Steps

1 Substitute s and r from the X intercept given

2 Expand X

3 Substitute y and x value given from point

4 Solve to find a

5 Re-assemble equation

Intercepts of quadratic and linear

-Solving for # of intersections

1 Combine the equations

2 Group like terms

3 Solve for X through Factoring or Quadratic Equation

-Working with Radicals