Consider the functions given by f(x) = 5-(x-1)2 and g(x)=4-x. a. Use algebra to find the...

 

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Consider the functions given by f(x) = 5-(x-1)2 and g(x)=4-x. a. Use algebra to find the points where the graphs of and g intersect. b. Sketch an accurate graph of and g on the axes provided, labeling the curves by name and the intersection points with ordered pairs. c. Find and evaluate exactly an integral expression that represents the area between y = f(x) and the x-axis on the interval between the intersection points off and g. d. Find and evaluate exactly an integral expression that represents the area between y = g(x) and the x-axis on the interval between the intersection points of f and g. e. What is the exact area between and g between their intersection points? Why? 6+ 4+ 2+ 2 w- 3 Figure 6.1.1: Axes for plotting and g in Preview Activity 6.1.1 Consider the functions given by f(x) = 5-(x-1)2 and g(x)=4-x. a. Use algebra to find the points where the graphs of and g intersect. b. Sketch an accurate graph of and g on the axes provided, labeling the curves by name and the intersection points with ordered pairs. c. Find and evaluate exactly an integral expression that represents the area between y = f(x) and the x-axis on the interval between the intersection points off and g. d. Find and evaluate exactly an integral expression that represents the area between y = g(x) and the x-axis on the interval between the intersection points of f and g. e. What is the exact area between and g between their intersection points? Why? 6+ 4+ 2+ 2 w- 3 Figure 6.1.1: Axes for plotting and g in Preview Activity 6.1.1