3 = Advanced Math 3 Fall Final Exam Review. Unit 1: If f(x) = x 2 + 3, g(x) = 3x + 1, and h(x) = x + 1, evaluate each.

Transcription

1 Advanced Math Fall Final Eam Review Name: Unit 1: If f() +, g() + 1, and h() + 1, evaluate each. 1. f(g()). f(h()). g(- 4) 4. Given ff() + 9, represent its inverse as a (a) graph, (b) chart, and (c) function. y (a) (b) (c) f() 5. Find the inverse of the function ff() Use properties of eponents to write in eponential form: Simplify: 4 yy yy 8. Use common bases to solve for Use common bases to solve for Solve for the value of

2 11. Write in logarithmic form: 8 1. Write in eponential form: log 4 64 Unit : 1. y ( ) 14. y y ( + 1)( ) 17. Find the verte of ff() Find the equation of the parabola with verte at ( 1, ) that passes through the point ( 5, 9). 19. Find the equation of the parabola with points ( 1, ), (0, 1), (, 9). Determine the zeros and their multiplicity for each function y 1. ( + 7) ( 5)( + 5)( 1) y. y ( + 6) ( ) 5 Describe the end behavior of each function.. y y y 1 6. Determine the end behavior of the function: ff() As, ff() and as, ff()

3 7. Write the equation of the polynomial function graphed below: 8. Is the function odd, even, or neither? ff() Given the roots (zeros) of the polynomial, write a function in standard form. Roots: 4,0,- Unit : Use the following information for 0 & 1: Given: ff() and gg() 5 0. Find: ff() gg() 1. Find: ff() gg(). Solve: ( + 1)( + 1) 0. Solve: Factor completely: Factor by grouping: ff() +

4 6. Factor by grouping: ff() Given the function: ff() with a factor of ( - 1), find all the remaining factors. 8. Let PP() Find the value of PP(4). What does this tell you about the factor ( 4)? Divide. 9. ( ) ( 5) 40. ( ) ( + 1) using synthetic division using long division or area model Unit 4: Simplifying and Multiplying Rational Epressions Simplify the following AND state the Domain: Domain: Domain: Dividing Rational Epressions Divide and simplify completely: ( )

5 Add/Subtract Fractions and Rational Epressions Add and Subtract Rational Epressions with Like Denominators 1. Make sure the denominators are the same.. Add or subtract the numerators (combine like terms) and keep the denominators the same.. Factor the numerator and/or denominator, if possible 4. Simplify, if possible Simplify the following completely: Add/Subtract UNLIKE Rational Epressions Add and Subtract Rational Epressions with Unlike Denominators 1. Determine the least common multiple to get a common denominator! You might need to factor each denominator first. Figure out which factor is missing and multiply the numerator and denominator by the missing factor(s).. Simplify the numerator (FOIL, distribute, combine like terms, etc). 4. Factor the numerator, if possible. 5. Simplify, if possible. Simplify the following rational epressions Solving a Rational Equation Solve: Solving Rational Equations Find the least common denominator (LCD) FRACTION BUSTERS: multiply every term by the LCD to eliminate the denominators Solve the new equation and check to make sure your solution works Be sure to watch for domain restrictions. Values of that are not possible

6 Horizontal Asymptotes (HA) y A Horizontal Asymptotes tells the end behavior of a function. To determine the y-value of the HA, we need to compare the powers of the numerator and denominator. Determine the horizontal asymptote: 54. f ( ) HORIZONTAL ASYMPTOTES 55. yy (+) (+11)(+44) If the powers are the same, divide the coefficients. If the powers are larger in the denominator, the HA is y 0. If the powers are larger in the numerator, there is no HA. 56. f ( ) Vertical Asymptotes (VA) VERTICAL ASYMPTOTES AND HOLES If a factor CANNOT be divided out and remains in the denominator, it creates a vertical asymptote. Holes If a factor CAN be divided out from the numerator and denominator, then it creates a hole. Determine the -values for any holes or asymptotes: f ( ) 58. g( ) 59. f ( ) ( )( ) ( )( ) Graph the Rational Function.