Teacher: Mr. Chafayay. Name: Class & Block : Date: ID: A. 3 Which function is represented by the graph?

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1 Teacher: Mr hafayay Name: lass & lock : ate: I: Midterm Exam Math III H Multiple hoice Identify the choice that best completes the statement or answers the question Which function is represented by the graph? Which is the y-intercept of the graph of the function f(x) = x? (0, ) (0, ) (, 0) (0, ) Which expression is another way to write a 9 b? a b 8 9 a b 9 a b 8 a b f(x) = x f(x) = x f(x) = x f(x) = x Which function has an inverse that is not a function? f(x) = x +8 g(x) = x x +6 h(x) = x j(x) = x

2 I: Which is the simplified form of m 7 m? m 6 m m 6 m m m m 6 What is another way to write the exponential function f(x) = x? f(x) = x f(x) = Ê Ë Á x ˆ f(x) = Ê Ë Á x ˆ f(x) = x 7 When the denominator of the expression 8 is rationalized, which is the result? 8 The formula to determine the balance of a compound-interest bank account after t years is P = P 0 (+ r n )nt, where P is the current balance, P 0 is the original principal, r is the annual interest rate written as a decimal, and n is the number of times per year that the interest is compounded Justin deposited $00 in a bank earning 8% interest compounded monthly To the nearest tenth of a year, how long will it take for his balance to reach $60? years 8 years years 6 years 9 Which transformations would produce the graph of g(x) = ( x ) from the graph of f(x) = x? Reflect the graph of f(x) about the y-axis and then dilate the resulting graph vertically by a factor of Reflect the graph of f(x) about the y-axis and then dilate the resulting graph vertically by a factor of Reflect the graph of f(x) about the y-axis and translate the graph up units Reflect the graph of f(x) about the x-axis and translate the graph down units 0 What is the range of the function f(x) = lnx? all positive real numbers all negative real numbers all non-negative real numbers all real numbers

3 I: If f(x) = e x, what is the domain of f (x)? all real numbers all real numbers less than zero all real numbers greater than zero all positive integers Which logarithmic equation is equivalent to Ê ˆ the exponential equation = 7 Ë Á 8? log log = = log 7 8 = log ( ) = 7 8 What is the domain of the function g(x) = log(x ) +? all real numbers greater than all real numbers greater than all real numbers less than all real numbers greater than or equal to If h(x) = x, which point lies on the graph of h (x)? (, ) Ê, ˆ Ë Á Ê, ˆ Ë Á (, ) Which logarithmic equation is equivalent to the exponential equation log 7 0 =? 7 = 0 0 = 7 7 = = 6 Which is the inverse of the logarithmic function f(x) = log 8 x? f (x) = log 8 x f (x) = log 8 ( x) f Ê (x) = ˆ x Ë Á 8 f (x) = 8 x 7 What is the exact value of log 6? 8 What is the exact value of ln e? 6

4 I: 9 What are all the solutions of the equation log x =? x = ±8 x = 8 x = 6 x = 0 If log x =, what is the value of x? x = 0 x = x = x = If log x =, what is the value of x? How can the expression lnx ln x be rewritten as a single logarithm? ln(x x) lnx ln( x) lnx Which function represents the principal over time for a continuous compound interest bank account with an initial principal of $800 and an interest rate of %, where t is the time in years after the account was opened? P = 800e 00t P = 800(00t) P = 800e t P = 800(0 00t ) x = 8 x = 8 x = 8 x = Standardized Test Which is a correct statement of a property of logarithms? log a xy = (log a x)(log a y) log a xy = log a x log a y log b xy = log b x +log b y log x 0 = What are all the solutions of the equation log x = log +log 7? x = 9, 9 x = 9 x = 8 The equation has no solutions 6 What is the solution of the equation log x =? x = x = x = x =

5 I: 7 Which is the expanded form of log y log +log y log z log +log y log z 0 log y z log y log z z? 8 Which is a correct statement of the change of base formula? log r = (log r)(log s) log r s = log s log r log r s = log r log s log r s = log s r 9 What are all the solutions of the equation log(x ) = log x +log(x +)? x = x = x =, The equation has no solutions 0 Which expression is equal to log? log8 log 6 log 8+ log 6 log log Which logarithmic equation is equivalent to the exponential equation 8 = 66? Which best describes the solution(s) of the equation ln(x ) = ln(9 x)? x =, x = ;(x = is extraneous) x = ;(x = is extraneous) x = What are the quotient and remainder when x +x 8 is divided by x +? quotient: x +x +6; remainder: 0 quotient: x +x 6; remainder: 6 quotient: x 6x 8; remainder: 0 quotient: x +x 6; remainder: 0 What is the remainder when x x 8x +6x +0 is divided by x? 9 Which describes the zeros of the polynomial function f(x) = x x +x? 0 (multiplicity one), (multiplicity two) 0 (multiplicity one), (multiplicity two) 0 (multiplicity one), (multiplicity one), (multiplicity two) 0 (multiplicity two), (multiplicity one) log 8 = 66 log 66 = 8 log 8 66 = log 66 = 8

6 I: 6 How many distinct (different) roots does the equation x 0x +x = 0 have? 0 What are the actual rational roots of the equation x x 9x x 0? one two three four,,,, ±i ±, ±, ±, ±0, ±0 7 Which polynomial division is represented by this synthetic division? x +9x dividedbyx + x +9x dividedbyx x +9x dividedbyx + x +9x dividedbyx 8 What are the possible rational roots of the equation 6x 7x 8x? Examine this synthetic division Which conclusion can you make based on this work? If f(x) = x x +6, then f( ) = If f(x) = x x +6, then f( ) = If f(x) = x x +6 is divided by x +, the remainder is If f(x) = x x +6 is divided by x, the remainder is ±6 ±6 ±, ±, ±, ±, ± 6, ±, ±, ± 6 ±6, ±, ±, ±, ±, ±, ± 6, ±, ± 6 9 Which polynomial is a factor of x x +x 7? x + x x + x 6

7 I: What is? =, = 7 7 What is? = 0 7 0, = The matrices cannot be multiplied because the matrices are different sizes Which two matrices can be added? =, = 7, = 8, = 0, E = and and and and E Which two matrices cannot be multiplied with either matrix first? =, = 7, = 8, = 0, E = and and and and E 7

8 6 What is the inverse of 0? 7 Solve the system of equations using ramer s Rule Ï Ô x +y = 7 Ì ÓÔ x y = 8 x =, y = x =, y = x =, y = x =, y = 8 What is the product of and? What is the determinant of the matrix? I: 0 Which of the following describes the zeros of the polynomial function h(x) = x 8x +8? (multiplicity two); (multiplicity two) 9 (multiplicity two); 9 (multiplicity two) (multiplicity four) (multiplicity four) 8

Final Exam A Name. 20 i C) Solve the equation by factoring. 4) x2 = x + 30 A) {-5, 6} B) {5, 6} C) {1, 30} D) {-5, -6} -9 ± i 3 14

Final Exam A Name. 20 i C) Solve the equation by factoring. 4) x2 = x + 30 A) {-5, 6} B) {5, 6} C) {1, 30} D) {-5, -6} -9 ± i 3 14 Final Exam A Name First, write the value(s) that make the denominator(s) zero. Then solve the equation. 1 1) x + 3 + 5 x - 3 = 30 (x + 3)(x - 3) 1) A) x -3, 3; B) x -3, 3; {4} C) No restrictions; {3} D)