Study Island Algebra 2 Standards at Risk
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1 Study Island Algebra 2 Standards at Risk Scatter Plots 1. The number of people who visited a state park each year is recorded. The scatter plot below shows the park's annual visitors over a nine-year period beginning in Which quadratic equation best represents the data? y = 10.2x x y = -10.2x x y = 10.66x x y = x x Radical & Rational Equations 2. Solve the following rational equation. = 5 = 9 = 7 = 4
2 Properties of Functions 3. Which of the following types of functions can be discontinuous? logarithmic rational linear exponential Scatter Plots 4. Choose the equation below which would be the line of best fit for the scatter plot. y = 1 / 4 x y = 3 / 8 x y = 5 / 8 x y = 3 / 4 x Nonlinear Functions 5. Solve the following equation for x. x 2-13x = 0 x = -7; x = 20 x = 7; x = -20 x = -7; x = -20 x = 7; x = 20
3 Generalize Patterns 6. The first five terms of a sequence are given below. 30, 34, 38, 42, 46,... Determine which of the following formulas gives the n th term of this sequence. 33-3n 34-4n n n Inverse & Composition of Functions 7. Nonlinear Functions 8. Solve for x in the following equation. log b (x) + log b (x + 4) = log b (21) x = -7 x = -7, 3 x = -6, 2 x = 3
4 Radical & Rational Equations 9. Solve for x. Radical & Rational Equations 10. Solve the following rational equation. = 36 = 72 = -72 = -36 Nonlinear Functions 11.
5 Properties of Functions 12. Which of the following functions has the most asymptotes (horizontal and vertical)? Generalize Patterns 13. What is the recursive formula for this sequence? 7, 21, 63, 189, 567,... a 1 = 7, a n = a n a 1 = 7, a n = a n-1 + 3n a 1 = 7, a n = 3 (a n-1 ) - 7 a 1 = 7, a n = 3 (a n-1 ) Properties of Functions 14. Which type of function has a constant rate of change? I. linear II. exponential III. rational IV. logarithmic I and III only II and IV only I, II, III, and IV I only
6 Scatter Plots 15. Choose the equation below which would be the line of best fit for the scatter plot. y = 1 / 2 x + 5 y = 2 / 5 x + 5 y = 3 / 4 x + 2 y = 1 / 2 x + 2 Radical & Rational Equations 16. Solve for x. Properties of Functions 17. Which type of function has a variable rate of change? I. linear II. exponential III. rational IV. logarithmic II, III, and IV only I, II, III, and IV II and IV only I only
7 Nonlinear Functions 18. Solve the following equation for x. x 2-11x + 24 = 0 x = -3; x = 8 x = 3; x = -8 x = 3; x = 8 x = -3; x = -8 Scatter Plots 19. The graph above shows a line of best fit for data collected on the blood pressure of patients in relation to age. What is the equation of the line of best fit?
8 Generalize Patterns 20. Define the sequence below recursively. a 1 = 1 a n = a n-1 + (1/3) n a 1 = 1 a n = 1 / 3 a n-1 a 1 = 1 a n = a n-1 + 1/3 a 1 = 1 a n = a n-1 + 1/3 n 1, 1 1 / 3, 1 2 / 3, 2, 2 1 / 3, 2 2 / 3, 3, 3 1 / 3... Nonlinear Functions 21. Solve for x. Inverse & Composition of Functions 22. What is the inverse of the function below?
9 Radical & Rational Equations 23. Solve for x. 25 no solution Scatter Plots 24. The graph above shows a line of best fit for the data collected at a batting cage for the number of hits in relation to the speed of the pitch. What is the equation of the line of best fit?
10 Inverse & Composition of Functions 25. Radical & Rational Equations 26. Solve for x. 33 Properties of Functions 27. Which of the following is a true statement regarding the two functions below over the interval (0, )? f(x) has a decreasing rate of change and g(x) has an increasing rate of change f(x) has an increasing rate of change and g(x) has a decreasing rate of change f(x) has a decreasing rate of change and g(x) has an decreasing rate of change f(x) has an increasing rate of change and g(x) has an increasing rate of change
11 Inverse & Composition of Functions 28. If f(x) and g(x) are defined as below, what is f(g(x))? Nonlinear Functions 29. Solve the following equation for x. x = -4; x = -15 x = 4; x = 15 3x = 4x x x = 15; x = -4 x = -15; x = 4 Scatter Plots 30. Steve graphed how long it takes to get through the grocery store line in relation to the number of registers that are open. What is the equation of the line of best fit above?
12 Generalize Patterns 31. What is the explicit formula for this sequence? 16, 24, 32, 40, 48,... a n = 23-7n a n = 8 + 8n a n = 24-8n a n = 9 + 7n Inverse & Composition of Functions 32. Inverse & Composition of Functions 33.
13 Generalize Patterns 34. What is the recursive formula for this sequence? 15, 10, 0, -15, -35,... a 1 = 15, a n = a n-1-5(n) a 1 = 15, a n = a n-1-5 a 1 = 15, a n = 5(a n-1 ) - (n-1) a 1 = 15, a n = a n-1-5(n-1) Properties of Functions 35. Which of the following graphs intersect the x-axis? I, II, III, and IV II, III, and IV only II only II and III only Generalize Patterns 36. Find the fifth term in the recursively defined sequence below if a 1 = 1. a n = 2 a n
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