Question

State whether each of the following functions are continuous or not for all values in their domain. Justify your answer. Complete parts​ (a) through​ (d).

​(a)

​ a(t)equals=altitude

of a skydiver t seconds after jumping from a plane.

Choose the correct answer below.

A.

The function​ a(t) is continuous because the​ skydiver's altitude remains constant.

B.

The function​ a(t) is continuous because the​ skydiver's altitude decreases as time​ increases, with no breaks in between.

C.

The function​ a(t) is discontinuous because the​ skydiver's parachute slows him down.

D.

The function​ a(t) is discontinuous because the​ skydiver's altitude is constantly changing.

​(b)

​n(t)equals=number

of quarters needed to park in a metered parking space for t minutes.

Choose the correct answer below.

A.

The function​ n(t) is discontinuous because the number of quarters must be a whole number.

B.

The function​ n(t) is discontinuous because the number of minutes must be a whole number.

C.

The function​ n(t) is continuous because the car is parked continuously for t minutes.

D.

The function​ n(t) is continuous because there is no limit on the number of quarters.

​(c)

​ T(t)equals=temperature

t minutes after midnight in Chicago on January 1.

Choose the correct answer below.

A.

The function​ T(t) is continuous because the temperature changes gradually as time​ increases, with no jumps in between.

B.

The function​ T(t) is continuous because the temperature is a constant.

C.

The function​ T(t) is discontinuous because the temperature changes quickly.

D.

The function​ T(t) is discontinous because the temperature varies throughout the night.

​(d)

​ p(t)equals=number

of points scored by a baseball player after t minutes of a baseball game.

Choose the correct answer below.

A.

The function​ p(t) is discontinuous because the number of points must be a whole number.

B.

The function​ p(t) is continuous because the t time is constantly increasing.

C.

The function​ p(t) is discontinuous because the number of minutes must be a whole number.

D.

The function​ p(t) is continuous because the number of points scored is constantly increasing.

Answer 1