Intervals on Which f is Increasing or Decreasing Consider the following. y = 3x³ + 33x² + 57x Find the critical numbers. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) X = Find the open intervals on which the function is increasing or decreasing. Use a graphing utility to verify your results. See Examples 4, 5, and 7. (Enter your answers using interval notation. If an answer does not exist, enter DNE.) increasing decreasing

Use the given graph of to determine the function's domain, range, x-intercept(s), y-intercept, and function values. Use interval notation for interval solutions. If multiple solutions exist, use a comma-separated list to enter the solutions. If a solution does not exist, enter DNE. Hint: The dashed horizontal line is referred to as a horizontal asymptote. The blue curve gets very close (infinitesimally close) to the dashed line, but never touches or crosses it. 10 -8 -6 Domain: Range: x-intercept(s): y-intercept f(1) = -2 10 01 8 6 4 C U 7 -4 -6 -8 -10 2 I U I 1 4 I t 6 I 1 8 10

Find the domain and range of the function f(æ) = Vx + 7. (HINT: you can't have a negative number inside the square root 2! Also, Link to a review of interval notation here) 2 The domain is x E (Enter your answer in interval notation) The range is Y E (Enter your answer in interval notation)

Locate any intercepts of the function.