Directions: Show ALL of you work to find the best answer for the following questions. x 1/ 2

Transcription

1 Algebra 2 Study Island 3d, f, j l-n, 4a-b, 6c-d Directions: Show ALL of you work to find the best answer for the following questions. Algebraic Expressions 1. x 1/ 2 Which of the following expressions is equivalent to the expression above? 1 / 2 x (x) (x) x -2 Quantitative Relationships 2. Pam invested money into a small stock market account. After several years of continued growth, the table below shows how much her investment earned. Investment Earnings Years Money Earned $31.25 $125 $500 $2,000 $8,000 Which of the following functions would best model the data above? exponential function constant function quadratic function linear function

2 Change in Parameters 3. The curve given by the equation y = 3x 2-2 is graphed above. How will the graph of the equation be affected if the equation is changed to y = -3x 2-2? The graph will be shifted down. The graph will be wider. The graph will open down. The graph will be the same. Inverse & Composition of Functions 4. If f(x) and g(x) are defined as below, what is f(g(x))?

3 Change in Parameters 5. The curve given by the equation y = 4 x - 3 is graphed above. How will the graph of the equation be affected if the equation is changed to y = 4 x - 1? The graph of the equation will increase at the same rate, but the graph and y-intercept will be shifted up. The graph will not change. The graph of the function will increase at a faster rate. The graph of the equation will increase at the same rate, but the graph and y-intercept will be shifted down. Nonlinear Systems of Equations 6. Which is the apparent solution set to the system of equations shown on the graph?

4 Inverse & Composition of Functions 7. Transformations 8. The graph of f(x) = 5x 3 is a of the graph of g(x) = x 3. translation dilation reflection rotation Transformations 9. The equation y = - 1 / 2 x + 2 is graphed below. If the graph is reflected across the x-axis, then which equation below represents the new graph? y = - 1 / 2 x - 2 y = 1 / 2 x + 2 y = 1 / 2 x - 2 y = - 1 / 2 x + 2

5 Scatter Plots 10. Choose the equation below which would be the line of best fit for the scatter plot. y = 2 / 5 x + 5 y = 3 / 4 x + 2 y = 1 / 2 x + 5 y = 1 / 2 x + 2 Probability 11. Jodie is conducting an experiment and has to make a free throw and throw a dart for a bullseye. The probability of accomplishing both is 4 out of 7. The probability of making the free throw is 13 out of 18. Given the free throw is made, what is the probability of hitting the bullseye?

6 Scatter Plots 12. The graph above shows a line of best fit for data collected on the number of tickets sold at a year-round waterpark as a function of the daily high temperature. What is the equation of the line of best fit? Exponential & Logarithmic Functions 13. Which statement describes the rate of change of the following function? f(x) = ( 1 / 4 ) x The function decreases for all x, decreasing faster when x > -4 than it does when x < -4. The function decreases for all x, decreasing faster when x < 1 than it does when x > 1. The function increases for all x, increasing faster when x < 1 than it does when x > 1. The function has a constant rate of change, decreasing for all x at a rate of 1 / 4.

7 Transformations 14. Changing the equation y = (x - 4) 3-2 to y = -(x - 4) 3-2 will change the graph by reflecting it across the line y = -2. line x = -4. y-axis. x-axis. Change in Parameters 15. Each of the following statements describes a transformation of the graph y = x. Which statement describes the graph of y = x ? It is the graph of x shifted 11 units right and 11 units up. It is the graph of x shifted 11 units left and 11 units down. It is the graph of x shifted 11 units left and 11 units up. It is the graph of x shifted 11 units right and 11 units down. Nonlinear Systems of Equations 16. What is the solution set to the following system of quadratic equations? y = x 2-2x - 4 y = 2x 2-9x + 6 {(2,2);(5,11)} {(2,31);(5,4)} {(2,-4);(5,11)} {(-2,-4);(-5,11)} Trigonometry 17. If x = 32.5 cm and z = 39.2 cm, what is the measure of angle?

8 Probability 18. Kevin went to the store to rent a DV There are 23 copies of the DVD he wants to rent and 4 of them are scratched to the point that they will skip. Given one person came in right before Kevin and grabbed a copy that does not skip, what is the probability that Kevin will grab a DVD that skips? 2 / 11 3 / 22 3 / 23 4 / 23 Algebraic Expressions 19. Evaluate the expression below for x = 1 and y = Trigonometry 20. If = 65 and h = 5 mm, what is the value of k to the nearest tenth of a millimeter? 11.8 mm 11.3 mm 5.5 mm 10.7 mm Inverse & Composition of Functions 21.

9 Nonlinear Systems of Equations 22. Solve the following system of equations. (4,18) and (9,63) (3,15) and (4,18) y = x 2-4x + 18 y = 3x + 6 (-3,-3) and (-4,-6) (3,15) and (-4,-6) Scatter Plots 23. 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 Quantitative Relationships 24. Look at the data in the table below. x y ,291 7,775 Which of the following models would do the best job of modeling the data above? constant model exponential model quadratic model linear model Algebraic Expressions 25. Rewrite the following expression with only positive exponents. x -6 y -5 z -6 x 6 y 10 z -3 1 x 12 y 15 z 3 z 3 x 12 y 15 1 x 12 y 15 z 9 1 y 5 z 3 Probability 26. Which of the following statements best describes probability distribution? The occurrence of one event does not affect the probability of another event. A function that displays each outcome of a random event with its probability. The set of all possible outcomes of an experiment. The probability that one event leads to another event.

11 Exponential & Logarithmic Functions 27. What is the x-intercept of the following function? 1 0 The function does not have an x-intercept. 7 Quantitative Relationships 28. Look at the data in the table below. x y Which of the following models would do the best job of modeling the data above? exponential model quadratic model linear model constant model Exponential & Logarithmic Functions 29. Between and, which function has an average rate of change that is less than that of? Trigonometry 30. If n = 44 mm and p = 67 mm, what is the measure of angle?