Review of Functions

1. PSHS 3RD YEAR MATH Session 1

2. Diagnostic - Answers 1. Evaluate the function for f(-1) if

3. 2. What is the sum h(x) + g(x) if h(x) = 5x – 1 and g(x) = 3x2 + 6x – 7 ?

4. 3. If F(x)= 2x + 3 and G(x) = 5x – 4, what is the composite function G(F(x))?

5. 4. What is the domain of the square root function ? DOMAIN The set of all possible values for x, OR The x-coordinates of the points of the graph of the function 2 ways to analyze: 1.) Knowing the graph of the function 2.) Using the given equation of the function

6. The graph of What are the x-coordinates of the points on the graph?  DOMAIN

7. The graph of DOMAIN of is at x=5 Courtesy of Wolfram Alpha: www/wolframalpha.com GENERAL EQUATION: h=horizontal shift

8. 1 -1 -2 5. Function or not?

9. 6. Find the inverse of the function . HOW TO GET 1.) Use y for “f(x)”. 2.) Switch x and y. 3.) Isolate y. 4.) This new y will be your

10. 7. Which of the following is NOT divisible by (x – 1) ? 3 Ways to answer: 1.) Using LONG division. 2.) Using SYNTHETIC division. 3.) Using the REMAINDER THEOREM. Remainder Theorem: Therefore, is divisible by (x - 1).

11. 8. What are the roots of the function ? ROOTS – also known as the x-coordinates of the x-intercepts, OR the solutions to the equation if h( x ) were equal 0. HOW DO WE GET THE x-intercepts? Let y = 0, meaning let h( x ) = 0.

12. Which is the correct set of roots of f( x )? x = -3, 0 and 5 OR x = -5, 0 and 3

13. 9. What is the equation of the line that passes through (5, -6) and is perpendicular to the line whose equation is ? Point (5, -6) is a point on the line we are looking for. Perpendicular means that the slopes of and the unknown line are NEGATIVE RECIPROCALS of each other.

15. 10.b. Graph the function.

16. 11. Given the function : Find the vertex of the parabola. 2 ways: 1.) Vertex-form of the quadratic equation. 2.) Use the vertex formula.

17. 11.b. Find the domain and range. Domain – set of all real numbers: Range – based on 2 things: 1.) the y-coordinate of the VERTEX of the parabola. 2.) the direction where the parabola is opening  leading coefficient. Therefore, the range is

18. 11.c. Graph the function. Vertex: (1, 2)

19. Trigonometric functions Sine, Cosine, and Tangent These are RATIOS of the sides of the right triangle SOH CAH TOA

20. RECALL: Pythagorean Theorem If side a = 5 cm. and side c = 13 cm., what is the length of side b? c a b where a and b are the LEGS, and c is the hypotenuse.

21. RECALL: The 30-60-90 TRIANGLE THEOREMS 60 c a 30 b The side opposite 30 degrees will have a length of ½ of the length of the longest side (hypotenuse). The side opposite 60 degrees will be times the length of the longest side.

22. RECALL: THE 45-45-90 TRIANGLE a a c In terms of the sides, what kind of triangle is the 45-45-90 triangle? The length of the longest side is times the length of a leg.

23. Trigonometric identities

24. THE UNIT CIRCLE For angle measures greater than 90 deg, we use REFERENCE ANGLES.

25. Reference angles Angle rotation starts from the positive x-axis, then moving counter-clockwise. The reference angle is measured from the x-axis. What is the reference Angle of the ff? 1.) 120 deg = 2.) 225 deg = 3.) 330 deg =

26. UNITS OF ANGLES: DEGREES & RADIANS

27. What IF YOU FORGOT THE CONVERSIONS? What is 270 degrees in radian measure? Just memorize one thing:

28. What are the trigonometric function values of the ff. angles?

29. Using the periodicity of the sine and cosine functions

30. GRAPHS OF THE TRIGONOMETRIC FUNCTIONS

31. FEATURES of y = sin x1. Amplitude2. Period3. Phase shift (horizontal)4. Vertical shift

36. Transformations of the graph a - amplitude k – Vertical shiftc c/b – Horizontal (phase) shift b/ (2pi) - Period