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# TIU CET Review Math Session 6 - part 2 of 2

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College Entrance Test Review
Math Session 6 - part 2 of 2
FUNCTIONS
How to evaluate
Operations on functions
Composite functions
Trigonometric Functions
Pythagorean Theorem
30 60 90 triangle
45 45 90 triangle
Exponential Functions
Logarithmic Functions

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### TIU CET Review Math Session 6 - part 2 of 2

1. 1. FUNCTIONS TIU College Entrance Test Review Math Session 6
2. 2. 1. Evaluate the function for f (-1) if Answers
3. 3. 2. What is the sum h(x) + g(x) if h(x) = 5x – 1 and g(x) = 3x 2 + 6x – 7 ?
4. 4. 3. If F(x)= 2x + 3 and G(x) = 5x – 4, what is the composite function G(F(x))?
5. 5. 4. What is the domain of the square root function ? <ul><li>DOMAIN </li></ul><ul><li>The set of all possible values for x, OR </li></ul><ul><li>The x-coordinates of the points of the graph of the function </li></ul>2 ways to analyze: 1.) Knowing the graph of the function 2.) Using the given equation of the function
6. 6. The graph of <ul><li>Courtesy of Wolfram Alpha: www/wolframalpha.com </li></ul><ul><li>GENERAL EQUATION: </li></ul>at x =5 h =horizontal shift DOMAIN of is
7. 7. 5. Function or not? Relation Function Not a Function <ul><ul><li>{(5,6), (-2,3), (3,1), (5,2), (8, -4) } </li></ul></ul>b. y = 9 – x 2 c. d. x = (y + 6) (y – 3) -1 1 -2
8. 8. 6. What are the roots of the function ? <ul><li>ROOTS – also known as the x-coordinates of the x-intercepts , OR the solutions to the equation if h( x ) were equal 0. </li></ul><ul><li>HOW DO WE GET THE x-intercepts? </li></ul><ul><li>Let y = 0, meaning let h( x ) = 0. </li></ul>
9. 9. Which is the correct set of roots of f( x ) ? x = -3, 0 and 5 OR x = -5, 0 and 3
10. 10. 7. Which of the following is NOT divisible by (x – 1) ? <ul><li>3 Ways to answer: </li></ul><ul><li>1.) Using LONG division. </li></ul><ul><li>2.) Using SYNTHETIC division. </li></ul><ul><li>3.) Using the REMAINDER THEOREM. </li></ul><ul><li>Remainder Theorem: </li></ul>Therefore, is divisible by ( x - 1).
11. 11. 7. What is the equation of the line that passes through (5, -6) and is perpendicular to the line whose equation is ? <ul><li>Point (5, -6) is a point on the line we are looking for. </li></ul><ul><li>Perpendicular means that the slopes of </li></ul><ul><li>and the unknown line are NEGATIVE RECIPROCALS of each other. </li></ul>
12. 12. 8. Given the function : <ul><li>Find the intercepts. </li></ul><ul><li>To get the x-intercept: </li></ul><ul><li>Therefore, </li></ul><ul><li>x-intercept = (1/2, 0). </li></ul><ul><li>To get the y-intercept: </li></ul>Therefore, y-intercept = (0, 1). Let y = 0, meaning let f ( x ) = 0. let x = 0
13. 13. 8.b. Graph the function.
14. 14. 9. Given the function : <ul><li>Find the vertex of the parabola. </li></ul><ul><li>2 ways: </li></ul><ul><li>1.) Vertex-form of the quadratic equation. </li></ul><ul><li>2.) Use the vertex formula. </li></ul>
15. 15. 9.b. Find the domain and range. <ul><li>Domain – set of all real numbers: </li></ul><ul><li>Range – based on 2 things: </li></ul><ul><li>1.) the y-coordinate of the VERTEX of the parabola. </li></ul><ul><li>2.) the direction where the parabola is opening  leading coefficient. </li></ul><ul><li>Therefore, the range is </li></ul>
16. 16. 9.c. Graph the function. Vertex: (1, 2)
17. 17. Trigonometric functions <ul><li>Sine, Cosine, and Tangent </li></ul><ul><li>These are RATIOS of the sides of the right triangle </li></ul>SOH CAH TOA
18. 18. RECALL: Pythagorean Theorem a b c If side a = 5 cm. and side c = 13 cm., what is the length of side b? where a and b are the LEGS, and c is the hypotenuse.
19. 19. RECALL: The 30-60-90 TRIANGLE THEOREMS <ul><li>The side opposite 30 degrees will have a length of ½ of the length of the longest side (hypotenuse). </li></ul><ul><li>The side opposite 60 degrees will be times the length of the longest side. </li></ul>30 60 a b c
20. 20. RECALL: THE 45-45-90 TRIANGLE <ul><li>In terms of the sides, what kind of triangle is the 45-45-90 triangle? </li></ul><ul><li>The length of the longest side is times the length of a leg. </li></ul>a c a
21. 21. Trigonometric identities
22. 22. THE UNIT CIRCLE For angle measures greater than 90 deg, we use REFERENCE ANGLES.
23. 23. 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 =
24. 24. UNITS OF ANGLES: DEGREES & RADIANS
25. 25. What IF YOU FORGOT THE CONVERSIONS? <ul><li>What is 270 degrees in radian measure? </li></ul><ul><li>Just memorize one thing: </li></ul>
26. 26. What are the trigonometric function values of the ff. angles? Angle Sin x Cos x Tan x Csc x Sec x Cot x 240 deg -225 deg -150 deg
27. 27. p. 132 Simplify <ul><li>The trick is to represent all functions in terms of sin x and cos x. </li></ul><ul><li>Recall the definitions of sec x, csc x, and cot x. </li></ul>
28. 30. EXPONENTIAL & LOGARITHMIC FUNCTIONS
29. 31. Example: Given . What is x? <ul><li>x = 4. </li></ul><ul><li>If the bases are the same, then the exponents will be equal also. </li></ul><ul><li>What is x? </li></ul>
30. 32. <ul><li>When the bases are the same, you can equate the exponents already. </li></ul>
31. 33. Another example: Solve for x
32. 35. THE LOGARITHMIC FUNCTION IS THE INVERSE OF THE EXPONENTIAL FUNCTION.
33. 36. <ul><li>EXPONENTIAL FORM </li></ul><ul><li>To what exponent will you raise 2 to get 8? </li></ul>base exponent power of 2 <ul><li>LOGARITHMIC FORM </li></ul>
34. 37. p. 132 examples
35. 38. Example of an exponential function & a logarithmic function