please help me with the questions below:
4. [0/3 Points] DETAILS PREVIOUS ANSWERS LARCAAPCALC2 7.2.018. MY NOTES A Consider the following. f( x ) = - x - 3 x2 - 9 Describe the interval(s) on which the function is continuous. (Enter your answer using interval notation.) Identify any discontinuities. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) X = X If the function has any discontinuities, identify the conditions of continuity that are not satisfied. (Select all that apply. Select each choice if it is met for O There is a discontinuity at x = c where f(c) is not defined. There is a discontinuity at x = c where lim f(x) = f(c). X - C There is a discontinuity at x = c where lim f(x) does not exist. X -C O There are no discontinuities; f(x) is continuous. X Need Help? Read It Watch It6. [-/3 Points] DETAILS LARCAAPCALC2 7.2.030.MI. Consider the following. A( x ) = 1 xz - 1 , X50 9x + 2, X 30 Describe the interval(s) on which the function is continuous. (Enter your answer using interval notation.) Identify any discontinuities. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) X = If the function has a discontinuity, identify the conditions of continuity that are not satisfied. There is a discontinuity at x = c where f(c) is not defined. O There are no discontinuities; f(x) is continuous. O There is a discontinuity at x = c where lim f(x) does not exist. X - C O There is a discontinuity at x = c where lim f(x) # f(c). X - C Need Help? Read It Watch It Master It7. [-/4 Points] DETAILS LARCAAPCALC2 7.2.061. M The cost C (in millions of dollars) of removing x percent of the pollutants emitted from the smokestack of a factory can be modeled by C = - 8X 100 - X (a) What is the implied domain of C? (Enter your answer using interval notation.) Explain your reasoning. O Negative x-values and values greater than 100 do not make sense in this context. Also, C(100) is undefined. O The function is defined for all x-values except x = 100. It would be cost prohibitive to remove more than 80% of the pollutants. O Since we are removing pollutants, only negative x-values make sense in this context. O You cannot remove 0% of the pollutants. (b) Use a graphing utility to graph the cost function. Is the function continuous on its domain? Explain your reasoning. O C is not continuous on its domain because C has a removable discontinuity at x = 8. C is continuous on its domain because all rational functions are continuous on their domains. O C is continuous on its domain because C is a polynomial. O C is not continuous on its domain because C has a nonremovable discontinuity at x = -8. O C is not continuous on its domain because C is not a polynomial. (c) Find the cost of removing 68% of the pollutants from the smokestack. million Need Help? Read It Watch It5. [-/3 Points] DETAILS LARCAAPCALC2 7.2.029. MY NOTES ASK YOUR TEACHER PRACTI Consider the following. f ( x ) = 3 +x, x5 2 (x2 + 1, x > 2 Describe the interval(s) on which the function is continuous. (Enter your answer using interval notation.) Identify any discontinuities. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) X = If the function has any discontinuities, identify the conditions of continuity that are not satisfied. (Select all that apply. Select each choice if it is met for any of the discontinuities.) O There is a discontinuity at x = c where f(c) is not defined. There is a discontinuity at x = c where lim f(x) = f(c). X - C O There is a discontinuity at x = c where lim f(x) does not exist. X - C There are no discontinuities; f(x) is continuous. Need Help? Read It Watch It
