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TIU CET Review Math Session 6 - part 2 of 2
 

TIU CET Review Math Session 6 - part 2 of 2

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College Entrance Test Review...

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 TIU CET Review Math Session 6 - part 2 of 2 Presentation Transcript

    • FUNCTIONS TIU College Entrance Test Review Math Session 6
    • 1. Evaluate the function for f (-1) if Answers
    • 2. What is the sum h(x) + g(x) if h(x) = 5x – 1 and g(x) = 3x 2 + 6x – 7 ?
    • 3. If F(x)= 2x + 3 and G(x) = 5x – 4, what is the composite function G(F(x))?
    • 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
    • The graph of
      • Courtesy of Wolfram Alpha: www/wolframalpha.com
      • GENERAL EQUATION:
      at x =5 h =horizontal shift DOMAIN of is
    • 5. Function or not? Relation Function Not a Function
        • {(5,6), (-2,3), (3,1), (5,2), (8, -4) }
      b. y = 9 – x 2 c. d. x = (y + 6) (y – 3) -1 1 -2
    • 6. 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.
    • Which is the correct set of roots of f( x ) ? x = -3, 0 and 5 OR x = -5, 0 and 3
    • 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).
    • 7. 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.
    • 8. Given the function :
      • Find the intercepts.
      • To get the x-intercept:
      • Therefore,
      • x-intercept = (1/2, 0).
      • To get the y-intercept:
      Therefore, y-intercept = (0, 1). Let y = 0, meaning let f ( x ) = 0. let x = 0
    • 8.b. Graph the function.
    • 9. Given the function :
      • Find the vertex of the parabola.
      • 2 ways:
      • 1.) Vertex-form of the quadratic equation.
      • 2.) Use the vertex formula.
    • 9.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
    • 9.c. Graph the function. Vertex: (1, 2)
    • Trigonometric functions
      • Sine, Cosine, and Tangent
      • These are RATIOS of the sides of the right triangle
      SOH CAH TOA
    • 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.
    • RECALL: The 30-60-90 TRIANGLE THEOREMS
      • 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.
      30 60 a b c
    • RECALL: THE 45-45-90 TRIANGLE
      • 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.
      a c a
    • Trigonometric identities
    • THE UNIT CIRCLE For angle measures greater than 90 deg, we use REFERENCE ANGLES.
    • 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 =
    • UNITS OF ANGLES: DEGREES & RADIANS
    • What IF YOU FORGOT THE CONVERSIONS?
      • What is 270 degrees in radian measure?
      • Just memorize one thing:
    • 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
    • p. 132 Simplify
      • The trick is to represent all functions in terms of sin x and cos x.
      • Recall the definitions of sec x, csc x, and cot x.
    •  
    •  
    • EXPONENTIAL & LOGARITHMIC FUNCTIONS
    • Example: Given . What is x?
      • x = 4.
      • If the bases are the same, then the exponents will be equal also.
      • What is x?
      • When the bases are the same, you can equate the exponents already.
    • Another example: Solve for x
    •  
    • THE LOGARITHMIC FUNCTION IS THE INVERSE OF THE EXPONENTIAL FUNCTION.
      • EXPONENTIAL FORM
      • To what exponent will you raise 2 to get 8?
      base exponent power of 2
      • LOGARITHMIC FORM
    • p. 132 examples
    • Example of an exponential function & a logarithmic function