The graphs of four functions f, g, h, and i are shown below. + 4y 3- -2 1 1 2 3 + + x 5 6 Read carefully: The functions below must be written in terms of f, g, h, or i as indicated. If your answer only includes the letter x without one of the functions indicated, it will not be answering the question correctly. Although you may realize that f(x) = x, use the general name for this function and not the x. The point of this question is to understand how transformations work on general functions, not just on specific functions. This kind of remark is typically not included in questions as the question does explicitly tell you how to write your answer. The remark is added here to help you learn as it addresses a common mistake on the midterm. a. Write g(x) in terms of transformations of f. Then g(x) = b. Write f(x) in terms of transformations of g. Then f(x) = c. Write h(x) in terms of transformations of f. Then h(x) = Preview Preview Preview d. Write i(x) in terms of vertical transformations of f that can only occur at integer multiples of 0.5 (so 0.5, -0.5, 1, etc). i(x): = Preview The graph of a polynomial function f is shown below. + 4y 3 2 -3 -2 -1 2 +1 -2 + 8 Answer the following questions and use them to help write an equation for f. If there is more than one answer, separate your answers with a comma. Assume the coefficient on the leading term has absolute value of 0.25 and that f only has real roots. a. The root(s) of f with odd multiplicity is (are) b. The root(s) of with even multiplicity is (are) c. The coefficient on the leading term is Preview Preview Preview d. Assume roots with odd or even multiplicity have multiplicity 1 or 2, respectively. Write an equation for f. f(x) = Preview = 16t + 37t + 120 determines the height of the snowball A snowball is thrown upward from a bridge into a river below. The function f(t) above the surface of the water (in feet) in terms of the number of seconds t since the snowball was thrown. To help you answer questions c. and d., remember that a parabola is symmetric about the vertical line through the vertex (axis of symmetry) and so both zeros off are the same distance from the axis of symmetry. Depict the path off the snowball by hand (do not use an external tool/grapher). a. What is the bridge's height above the water? feet Preview b. How many seconds after being thrown does the snowball hit the water? seconds Preview c. How many seconds after being thrown does the snowball reach its maximum height above the water? seconds Preview d. What is the snowball's maximum height above the water? feet Preview The graph of a quadratic function f is shown below. 4y 3 2 x -4 -2 -1 3 4 N + Answer the following questions and use them to help write an equation for f. If there is more than one answer, separate your answers with a comma. a. The roots of are -3, 1 Preview b. The coordinates, (x, y), of the vertex of f is (-1,-2) c. The coefficient on x2 is: 1 d. Write an equation for f. f(x) = = (x+1)^2+2x-3 Preview Preview Preview