Answer Happy

1. (15 points) Consider the function given by: g(x) = {{ x² √x -x+4 a. Sketch the graph of g(x). b. State the domain and range of g(x). Write your answers in interval notation using the fewest number of intervals possible. Domain: Range: c. State the intervals on which g(x) is increasing and the intervals on which g(x) is decreasing. Write your answers in interval notation using the fewest number of intervals possible. if -2 ≤ x < 0 if 0 < x < 4 if x 24 -5 Concave down: 0 -5- Increasing: Decreasing: d. State the intervals on which g(x) is concave up and the intervals on which g(x) is concave down. Write your answers in interval notation using the fewest number of intervals possible. Concave up: e. Use your graph to solve g(x) = 0. f. How many solutions does the equation g(x) = 2 have? g. Calculate the average rate of change of g(x) on the interval [1,4].