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Pre-Calculus Mid-Term Exam Review Name ___________________________________ Pd ___ Chapter 1: Functions Determine whether the following relations are functions. 1) {(0, -3), (4, 6), (0, 4)} 2) {(5, 3), (2, 3)} 3) 4) For f(x) = 2x2 – x and g(x) = x + 6, find the following values. 5) f(g(x)) 6) g(f(x)) 7) f(t-3) 8) g(f(3)) Determine whether the given function is even, odd, or neither. 9) 10) 11) 12) For each graph below, determine the domain, range, y-intercept, zeros (x-intercepts), continuity, maximums and minimums, intervals of increasing and decreasing, asymptotes, and end behavior. If the characteristic is not present, write N/A. 13) 14) 15) 𝒙 + 𝟐 𝒊𝒇 𝒙 ≤ 𝟎 Use the piecewise function 𝒇(𝒙) = { for questions 16-19. −𝒙𝟐 𝒊𝒇 𝒙 > 𝟎 16) Graph the function on the grid provided. 17) Find f(-2) 18) Find f(0) 19) Find f(1) If f(x) = x2 is the parent graph, describe how the following graphs are transformed. 20) (x + 2)2 - 4 21) –x2 22) x-2 23) x2 + 5 d) c 24) Sketch the following parent functions on the grid provided. a) x b) x2 c) x3 e) log 𝑏 𝑥 f) √𝑥 g) 𝑥 1 h) bx Chapter 2 For each polynomial, determine whether the degree is even or odd AND whether the leading coefficient is positive or negative. 25) 26) 27) 28) Determine the horizontal asymptote(s), the vertical asymptote(s), and the hole(s) for the following functions. 29) 𝑓(𝑥) = 𝑥+4 −2𝑥−6 30) 𝑔(𝑥) = 2𝑥+6 𝑥 2 +𝑥−6 31) ℎ(𝑥) = 𝑥 3 −𝑥 2 −6𝑥 −3𝑥 2 −3𝑥+18 Solve each equation. 32) √2𝑥 − 7 + 3 = 𝑥 33) 34) 35) Chapter 3 Evaluate each logarithm. 36) 37) 38) 39) Solve each equation. (ISOLATE!!!) 40) 2𝑒 𝑥 + 4 = 10 41) 3x-1 = 25 42) 4log 4x – 1 = 7 43) 5 ln x = 50 44) In 2008, the raccoon population in a certain area was 15,000. The number of raccoons decreases exponentially at a rate of 8% per year. Predict the population in 2014. 45) Ellen is investing $1,500 in an account that earns an APR of 5% interest. a) How much is the account worth in 15 years if it is compounded monthly? b) How much is the account worth in 15 years if it is compounded daily? c) How much is the account worth in 15 years if it is compounded continuously? 46) The city of Sugar Land has been experiencing rapid growth as shown in the table below. Year 1980 1981 1982 1983 1984 1985 Population 18,940 21,150 23,490 27,570 29,610 35,480 a) Find an exponential regression equation that models this data. b) Use the exponential regression equation to predict the population in 1990. c) Use the exponential regression equation to predict when the population will reach 100,000.