Let f(x) be a function on which a transformation occurs. Let g(x) be a transformation of...

  

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Let f(x) be a function on which a transformation occurs. Let g(x) be a transformation of f. For each problem, name the transformation(s) that would map f(x) onto g(x). a) f(x)=8* and g(x) = 2* b) f(x)=3x and g(x) = -2f(x) c) f(x)=3x and g(x)=(f(x))-2 88 A lake in the Cascade Mountains has frozen over during the winter. As spring brings warmer weather, the ice sheet begins to melt. The table below gives the area of the ice, is square feet, at various times, in days since the beginning of spring. Time (days) Area 0 1 2 2.5 2 1.6 (millions of square feet) The area of the ice can be modeled by the function A(t) = ab, where A(t) is the area, in square feet, at time t days since the beginning of spring. a. Use the given data to write two equations that can be used to find the values for constants a and b in the expression A(t). b. Find the values for a and b, then write the expression for A(t). c. Use the given data to find the average rate of change of the area from t = 0 to t = 2 days. Show the computations that lead to your answer. d. Interpret the meaning of your answer from part e in the context of the problem. Let f(x) be a function on which a transformation occurs. Let g(x) be a transformation of f. For each problem, name the transformation(s) that would map f(x) onto g(x). a) f(x)=8* and g(x) = 2* b) f(x)=3x and g(x) = -2f(x) c) f(x)=3x and g(x)=(f(x))-2 88 A lake in the Cascade Mountains has frozen over during the winter. As spring brings warmer weather, the ice sheet begins to melt. The table below gives the area of the ice, is square feet, at various times, in days since the beginning of spring. Time (days) Area 0 1 2 2.5 2 1.6 (millions of square feet) The area of the ice can be modeled by the function A(t) = ab, where A(t) is the area, in square feet, at time t days since the beginning of spring. a. Use the given data to write two equations that can be used to find the values for constants a and b in the expression A(t). b. Find the values for a and b, then write the expression for A(t). c. Use the given data to find the average rate of change of the area from t = 0 to t = 2 days. Show the computations that lead to your answer. d. Interpret the meaning of your answer from part e in the context of the problem.