Senor Pablo Tricks and Trivia: Grade 11 Periodic Test Review

Introduction

• Welcome message by Senor Pablo.
• Review and solve questions from the first periodic test in Grade 11 General Mathematics.
• Questions can be found in the community section on Senor Pablo TV.

Key Concepts

1. Defining Functions:

   • A set is a function if no x-coordinate is repeated.
   • Example: Choice B (x = 1, 2, 3, 4 with no repetitions) defines a function.

2. Vertical Line Test:

   • Used to determine if a graph defines a function.
   • Example: For each x-value, should only intersect the graph once (Choice B).

3. Arrow Diagrams & Functions:

   • One-to-One or Many-to-One:
     • Function: Each x maps to exactly one y.
     • Non-function: Mapping should not be Many-to-One.
   • Example: Choice C (one-to-many) defines a function.

4. Graphs and Functions:

   • Use the vertical line test to identify graphs that do not define a function.
   • Example: Graph D fails the test as it intersects twice for some x-values.

5. Finding f(x):

   • Problem: f(x) = 4x^2 + 3x - 15 at x = -2:
     • Calculation:
       • 4*(-2)^2 + 3*(-2) - 15
       • = 16 - 6 - 15
       • = -5
     • Example: Result is -5 (Choice D).

6. Finding Range of a Function:

   • Function: f(x) = x/2 + 3 for given x-values 0, 2, 4, 6, 8:
     • Calculations:
       • f(0) = 3, f(2) = 4, f(4) = 5, f(6) = 6, f(8) = 7
     • Example: Range is {3, 4, 5, 6, 7} (Choice D).

7. Composite Functions:

   • Find value of composite functions f(g(3)) given:
     • f(x) = x^4 - 1
     • g(x) = x - 2
   • Calculation:
     • g(3) = 1
     • f(1) = 1^4 - 1 = 0
     • Example: Result is 0 (Choice C).

8. Undefined Products:

   • Determine x for which product f(x) * g(x) is undefined when denominators are zero.
   • Given functions:
     • f(x) = 3x/(x-2)
     • g(x) = (2x-1)/(x-2)
     • Example: Denominators zero for x = 2; product undefined (Choice C).*

Summary of Answers

• Question 1: B
• Question 2: B
• Question 3: C
• Question 4: D
• Question 5: D
• Question 6: D
• Question 7: C
• Question 8: C

Conclusion

• Stay tuned for part 2 of the periodic test review.
• Next video on Saturday.

[Applause]