Solved: In Exercises 1134, describe the interval(s) on which the function is continuous

In Exercises 110, determine whether the function is continuous on the entire real line. Explain your reasoning.

In Exercises 110, determine whether the function is continuous on the entire real line. Explain your reasoning.

In Exercises 110, determine whether the function is continuous on the entire real line. Explain your reasoning.

In Exercises 110, determine whether the function is continuous on the entire real line. Explain your reasoning.

In Exercises 110, determine whether the function is continuous on the entire real line. Explain your reasoning.

In Exercises 110, determine whether the function is continuous on the entire real line. Explain your reasoning.

In Exercises 110, determine whether the function is continuous on the entire real line. Explain your reasoning.

In Exercises 110, determine whether the function is continuous on the entire real line. Explain your reasoning.

In Exercises 110, determine whether the function is continuous on the entire real line. Explain your reasoning.

In Exercises 110, determine whether the function is continuous on the entire real line. Explain your reasoning.

In Exercises 1134, describe the interval(s) on which the function is continuous. Explain why the function is continuous on the interval(s). If the function has a discontinuity, identify the conditions of continuity that are not satisfied.

In Exercises 1134, describe the interval(s) on which the function is continuous. Explain why the function is continuous on the interval(s). If the function has a discontinuity, identify the conditions of continuity that are not satisfied.

In Exercises 1134, describe the interval(s) on which the function is continuous. Explain why the function is continuous on the interval(s). If the function has a discontinuity, identify the conditions of continuity that are not satisfied.

In Exercises 1134, describe the interval(s) on which the function is continuous. Explain why the function is continuous on the interval(s). If the function has a discontinuity, identify the conditions of continuity that are not satisfied.

In Exercises 1134, describe the interval(s) on which the function is continuous. Explain why the function is continuous on the interval(s). If the function has a discontinuity, identify the conditions of continuity that are not satisfied.fx  x2  2x  1

In Exercises 1134, describe the interval(s) on which the function is continuous. Explain why the function is continuous on the interval(s). If the function has a discontinuity, identify the conditions of continuity that are not satisfied.fx  3  2x  x2

In Exercises 1134, describe the interval(s) on which the function is continuous. Explain why the function is continuous on the interval(s). If the function has a discontinuity, identify the conditions of continuity that are not satisfied.fx  x x2  1

In Exercises 1134, describe the interval(s) on which the function is continuous. Explain why the function is continuous on the interval(s). If the function has a discontinuity, identify the conditions of continuity that are not satisfied.fx  x  3 x2  9

In Exercises 1134, describe the interval(s) on which the function is continuous. Explain why the function is continuous on the interval(s). If the function has a discontinuity, identify the conditions of continuity that are not satisfied.fx  x x2  1

In Exercises 1134, describe the interval(s) on which the function is continuous. Explain why the function is continuous on the interval(s). If the function has a discontinuity, identify the conditions of continuity that are not satisfied.fx  1 x2  1

In Exercises 1134, describe the interval(s) on which the function is continuous. Explain why the function is continuous on the interval(s). If the function has a discontinuity, identify the conditions of continuity that are not satisfied.fx  x  5 x2  9x  20

In Exercises 1134, describe the interval(s) on which the function is continuous. Explain why the function is continuous on the interval(s). If the function has a discontinuity, identify the conditions of continuity that are not satisfied. fx  x  1 x2  x  2

In Exercises 1134, describe the interval(s) on which the function is continuous. Explain why the function is continuous on the interval(s). If the function has a discontinuity, identify the conditions of continuity that are not satisfied.

In Exercises 1134, describe the interval(s) on which the function is continuous. Explain why the function is continuous on the interval(s). If the function has a discontinuity, identify the conditions of continuity that are not satisfied.fx  x 2

In Exercises 1134, describe the interval(s) on which the function is continuous. Explain why the function is continuous on the interval(s). If the function has a discontinuity, identify the conditions of continuity that are not satisfied.fx 2x  3, x2, x < 1 x 1

In Exercises 1134, describe the interval(s) on which the function is continuous. Explain why the function is continuous on the interval(s). If the function has a discontinuity, identify the conditions of continuity that are not satisfied.fx 3  x, x2  1, x 2 x > 2

In Exercises 1134, describe the interval(s) on which the function is continuous. Explain why the function is continuous on the interval(s). If the function has a discontinuity, identify the conditions of continuity that are not satisfied.fx 1 2x  1, 3  x, x 2 x > 2

In Exercises 1134, describe the interval(s) on which the function is continuous. Explain why the function is continuous on the interval(s). If the function has a discontinuity, identify the conditions of continuity that are not satisfied.fx x2  4, 3x  1, x 0 x > 0

In Exercises 1134, describe the interval(s) on which the function is continuous. Explain why the function is continuous on the interval(s). If the function has a discontinuity, identify the conditions of continuity that are not satisfied.fx  x  1 x  1

In Exercises 1134, describe the interval(s) on which the function is continuous. Explain why the function is continuous on the interval(s). If the function has a discontinuity, identify the conditions of continuity that are not satisfied.fx  4  x 4  x

In Exercises 1134, describe the interval(s) on which the function is continuous. Explain why the function is continuous on the interval(s). If the function has a discontinuity, identify the conditions of continuity that are not satisfied.fx  x  1

In Exercises 1134, describe the interval(s) on which the function is continuous. Explain why the function is continuous on the interval(s). If the function has a discontinuity, identify the conditions of continuity that are not satisfied.fx  x  x

In Exercises 1134, describe the interval(s) on which the function is continuous. Explain why the function is continuous on the interval(s). If the function has a discontinuity, identify the conditions of continuity that are not satisfied.

In Exercises 1134, describe the interval(s) on which the function is continuous. Explain why the function is continuous on the interval(s). If the function has a discontinuity, identify the conditions of continuity that are not satisfied.

In Exercises 3538, discuss the continuity of the function on the closed interval. If there are any discontinuities, determine whether they are removable. Function Interval

In Exercises 3538, discuss the continuity of the function on the closed interval. If there are any discontinuities, determine whether they are removable. Function Interval

In Exercises 3538, discuss the continuity of the function on the closed interval. If there are any discontinuities, determine whether they are removable. Function Interval

In Exercises 3538, discuss the continuity of the function on the closed interval. If there are any discontinuities, determine whether they are removable. Function Interval

In Exercises 3944, sketch the graph of the function and describe the interval(s) on which the function is continuous.

In Exercises 3944, sketch the graph of the function and describe the interval(s) on which the function is continuous.

In Exercises 3944, sketch the graph of the function and describe the interval(s) on which the function is continuous.fx  x3  x x

In Exercises 3944, sketch the graph of the function and describe the interval(s) on which the function is continuous.fx  x  3 4x2  12x

In Exercises 3944, sketch the graph of the function and describe the interval(s) on which the function is continuous.fx x2  1, x  1, x < 0 x 0

In Exercises 3944, sketch the graph of the function and describe the interval(s) on which the function is continuousfx x2  4, 2x  4, x 0 x > 0

In Exercises 45 and 46, find the constant (Exercise 45) and the constants and (Exercise 46) such that the function is continuous on the entire real line.

In Exercises 45 and 46, find the constant (Exercise 45) and the constants and (Exercise 46) such that the function is continuous on the entire real line.

In Exercises 4752, use a graphing utility to graph the function. Use the graph to determine any x-value(s) at which the function is not continuous. Explain why the function is not continuous at the x-value(s).hx  1 x2  x  2

In Exercises 4752, use a graphing utility to graph the function. Use the graph to determine any x-value(s) at which the function is not continuous. Explain why the function is not continuous at the x-value(s).kx  x  4 x2  5x  4

In Exercises 4752, use a graphing utility to graph the function. Use the graph to determine any x-value(s) at which the function is not continuous. Explain why the function is not continuous at the x-value(s).fx 2x  4, x2  2x, x 3 x > 3

In Exercises 4752, use a graphing utility to graph the function. Use the graph to determine any x-value(s) at which the function is not continuous. Explain why the function is not continuous at the x-value(s).fx 3x  1, x  1, x 1 x > 1

In Exercises 4752, use a graphing utility to graph the function. Use the graph to determine any x-value(s) at which the function is not continuous. Explain why the function is not continuous at the x-value(s).fx  x  2x

In Exercises 4752, use a graphing utility to graph the function. Use the graph to determine any x-value(s) at which the function is not continuous. Explain why the function is not continuous at the x-value(s).fx  2x  1

In Exercises 5356, describe the interval(s) on which the function is continuous.

In Exercises 5356, describe the interval(s) on which the function is continuous.

In Exercises 5356, describe the interval(s) on which the function is continuous.

In Exercises 5356, describe the interval(s) on which the function is continuous.

Writing In Exercises 57 and 58, use a graphing utility to graph the function on the interval Does the graph of the function appear to be continuous on this interval? Is the function in fact continuous on Write a short paragraph about the importance of examining a function analytically as well as graphically.

Writing In Exercises 57 and 58, use a graphing utility to graph the function on the interval Does the graph of the function appear to be continuous on this interval? Is the function in fact continuous on Write a short paragraph about the importance of examining a function analytically as well as graphically.

Compound Interest A deposit of $7500 is made in an account that pays 6% compounded quarterly. The amount in the account after years is (a) Sketch the graph of Is the graph continuous? Explain your reasoning. (b) What is the balance after 7 years?

Environmental Cost The cost (in millions of dollars) of removing percent of the pollutants emitted from the smokestack of a factory can be modeled by (a) What is the implied domain of Explain your reasoning. (b) Use a graphing utility to graph the cost function. Is the function continuous on its domain? Explain your reasoning. (c) Find the cost of removing 75% of the pollutants from the smokestack.

Consumer Awareness A shipping companys charge for sending an overnight package from New York to Atlanta is $12.80 for the first pound and $2.50 for each additional pound or fraction thereof. Use the greatest integer function to create a model for the charge C for overnight delivery of a package weighing pounds. Use a graphing utility to graph the function, and discuss its continuity.

Consumer Awareness The United States Postal Service first class mail rates are $0.41 for the first ounce and $0.17 for each additional ounce or fraction thereof up to 3.5 ounces. A model for the cost (in dollars) of a first class mailing that weighs 3.5 ounces or less is given below. (Source: United States Postal Service) (a) Use a graphing utility to graph the function and discuss its continuity. At what values is the function not continuous? Explain your reasoning. (b) Find the cost of mailing a 2.5-ounce letter.

Salary Contract A union contract guarantees a 9% yearly increase for 5 years. For a current salary of $28,500, the salaries for the next 5 years are given by where represents the present year. (a) Use the greatest integer function of a graphing utility to graph the salary function, and discuss its continuity. (b) Find the salary during the fifth year (when ).

Inventory Management The number of units in inventory in a small company is where the real number is the time in months. (a) Use the greatest integer function of a graphing utility to graph this function, and discuss its continuity. (b) How often must the company replenish its inventory?

Owning a Franchise You have purchased a franchise. You have determined a linear model for your revenue as a function of time. Is the model a continuous function? Would your actual revenue be a continuous function of time? Explain your reasoning.

Biology The gestation period of rabbits is about 29 to 35 days. Therefore, the population of a form (rabbits home) can increase dramatically in a short period of time. The table gives the population of a form, where is the time in months and is the rabbit population. Graph the population as a function of time. Find any points of discontinuity in the function. Explain your reasoning.

Profit Consider the profit function for the manufacturer in Section 1.4, Exercise 71(b). Is the function continuous at Explain.