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Homework answers / question archive / consider the following two statements: (i) g is f reflected about the y—axis (ii) h is fcompressed vertically by a factor of; (a) (i) and (ii) are both true (b) (i) and (ii) are both false (c) (i) is true and (ii) is false ) (d) (i is false and (ii) is true 2

consider the following two statements: (i) g is f reflected about the y—axis (ii) h is fcompressed vertically by a factor of; (a) (i) and (ii) are both true (b) (i) and (ii) are both false (c) (i) is true and (ii) is false ) (d) (i is false and (ii) is true 2.The graph ofg(x) is the graph off(x) reflected vertically, stretched vertically by a factor of 2, and shifted downward 3 units. Write the equation ofg(x) in terms off(x). 3.Given the parent function, f(x) = x3, explain (in correct order) what transformations to f(x) have occurred to create the graph of the function g(x) = 3(x — 1)3 + 4. 4. g(x) is a transformation off(x) .The graph shows f(x) as a solid line and g(x) as a dotted line. What is g(x) in terms off(x)? (a) -3f(x) (b) f (-336) (C) 3f (x) (d) None of the above _\

13. Choose the letter of the function that isn't a polynomial function (a) f (x) =-2x2 - 7 (b) f (x ) = 2x2 - 5x-1+2 (c) f (x ) = x4 - 3x2 ( d) f (x) = 2 14. Use the graph to answer the following (2,72) (-2,0) (0,0) 5,0) (a) Estimate the extrema. Label each point as an absolute or relative max/min. (b ) List the intervals where the function is increasing (c) List the intervals where the function is decreasing. (d) List the intervals where the function is concave up e) List the intervals where the function is concave down 15. Write an equation to model the graph in vertex form, f(x) = a(x - h)2 + k, where a = 5. Hint: Put in all the pieces you know. You know a point on the graph (look at it closely). You know a. And that -20 is important. DID -20

9. B(w) is a function which gives the batted ball speed (in MPH) for various bat weights (in ounces) for Major League Baseball players in 2007. (a) B(w) can be modeled by the formula B(w) = —0.0257wz + 2.08929w + 36.7429. Compute the average rate of change for the weights w = 22 and w = 39 and explain what this number means in the real—world context. (Solution rounded to 3 decimal places) (b) Using B(w) = —O.0257W2 + 2.08929w + 36.7429, estimate the instantaneous rate of change for a bat weight of 47 ounces and explain what this number means in the real—world context. (Solution rounded to 3 decimal places) 10. The following table gives the number of Aerospace Products and Parts Industry Employees (in thousands), E, in the years since 1990. Years Since 1990 Aerospace Products x and Parts Industry Employees (in thousands) E 0 841 10 517 470 (a) Use quadratic regression to find the quadratic model that best fits the data (round to 3 decimal places) (b) Use the model to find E(7). Explain what the solution means in its real world context. (c) Perform a linear regression on this data. State the coefficient of determination (r2) for both the quadratic and linear regression. Which regression is a better fit? 11. The population of a city (in thousands) is given below, t years after 2007: P(t) = .071:2 + 4t + 110 a. Find the vertex and explain its meaning in the context of this situation b. Rewrite the function in vertex form 12. A missile is fired from a seaside cliff 300 ft above sea level at a 45° incline and a muzzle velocity of 75 ft/sec. The height ofthe missile above the water is modeled by h(x) = —0.00569x2 + x + 300 where x is the horizontal distance from the cliff face. a. At what horizontal distance from the cliff is the missile at its maximum height? b. Find the maximum height c. When the missile is 50ft above sea level, how far is it from the cliff?

x f (x) 906) -2 o 4 -1 3 3 o 2 1 1 2 -2 3 —8 Which is a good estimate of the instantaneous rate of change ofg(x) at x = —1? (a) 3 (b) -1 (C) 4 (d) none ofthe above 6. Based on data from 1980 to 2004, the number of Medicare enrollees (in millions) can be modeled by M(t) = —0.00472t2 + 0.6631: + 28.4 where t is the number of years since 1980. Find and explain the meaning of the vertical intercept ofthis model. 7. Suppose (1,3) is a point on the graph off(x). (3) Where does the point (1,3) from f(x) get transformed to in the graph off(x + 3) — 5? (b) Where does the point (1,3) from f(x) get transformed to in the graph of —4f(x)? (c) Where does the point (1,3) from f(x) get transformed to in the graph of 2f(x) + 8 8. Use the values shown in the following table to evaluate each expression. x f (x) -3 14 -2 11 -1 10 0 12 1 16 2 22 3 31 (a) 4f(x) whenx = —1 (b) —f(x+4) whenx =—2 (c) 3f(—x)+7whenx=3 (d) Solve forx: 0.5f(x — 3) = 11