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Chapter 2: Q. 6 (page 100)

True or False The cube function is odd and is increasing on the interval (-鈭�,鈭�).

Short Answer

Expert verified

The statement 'The cube function is odd and is increasing on the interval (-鈭�,鈭�).' is true.

Step by step solution

01

Step 1. Given information

We have been given a statement 'The cube function is odd and is increasing on the interval (-鈭�,鈭�).'

We have to tell whether this statement is true or false.

02

Step 2. Check for the odd function

The cube function is f(x)=x3.

Find f(-x).

f(-x)=(-x)3 f(-x)=-x3f(-x)=-f(x)

Therefore, the function is odd.

03

Step 3. Analyze the graph of cube function

The graph of cube function is:

It is clear from the graph that the cube function is increasing everywhere.

Therefore, the given statement is true.

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Most popular questions from this chapter

Wind Chill The wind chill factor represents the equivalent air temperature at a standard wind speed that would produce the same heat loss as the given temperature and wind speed. One formula for computing the equivalent temperature is

W={t0鈮�v<1.7933-(10.45+10v-v)(33-t)22.04,1.79鈮�v鈮�2033-1.5958(33-t),v>20

where vrepresents the wind speed (in meters per second) and trepresents the air temperature . Compute the wind chill for the following:

(a) An air temperature of localid="1645962228946" 10掳Cand a wind speed of 1 meter per second localid="1645962235368" (m/sec)

(b) An air temperature of localid="1645962241584" 10掳Cand a wind speed of localid="1645962248218" 5m/sec

(c) An air temperature of localid="1645962254138" 10掳Cand a wind speed of localid="1645962259043" 15m/sec

(d) An air temperature of localid="1645962265610" 10掳Cand a wind speed of localid="1645962274629" 25m/sec

(e) Explain the physical meaning of the equation corresponding to localid="1645962280348" 0鈮�v<1.79

(f) Explain the physical meaning of the equation corresponding to localid="1645962285160" v>20.

According to physicist Peter Brancazio, the key to a successful foul shot in basketball lies in the

arc of the shot. Brancazio determined the optimal angle of the arc from the free-throw line to be 45 degrees. The arc also depends on the velocity with which the ball is shot. If a player shoots a foul shot, releasing the ball at a 45-degree angle from a position 6 feet above the floor, then the path of

the ball can be modeled by the function

h(x)=-44x2v2+x+6

where h is the height of the ball above the floor, x is the forward distance of the ball in front of the foul line, and v is the initial velocity with which the ball is shot in feet per second. Suppose a player shoots a ball with an initial velocity of 28 feet per second.

(a) Determine the height of the ball after it has traveled 8 feet in front of the foul line.

(b) Determine h(12). What does this value represent?

(c) Find additional points and graph the path of the basketball.

(d) The center of the hoop is 10 feet above the floor and 15 feet in front of the foul line. Will the ball go through the hoop? Why or why not? If not, with what initial velocity must the ball be shot in order for the ball to go through the hoop?

Match each of the following functions with the graph that best describes the situation.

(a) The cost of building a house as a function of its square footage.

(b) The height of an egg dropped from a 300-foot building as a function of time.

(c) The height of a human as a function of time.

(d) The demand for Big Macs as a function of price.

(e) The height of a child on a swing as a function of time?

Reading and Interpreting Graphs Let C be the function whose graph is given below. This graph represents the cost C of using m anytime cell phone minutes in a month for a five-person family plan.

(a) Determine C(0). Interpret this value.

(b) Determine C(1000). Interpret this value.

(c) Determine C(2000). Interpret this value.

(d) What is the domain of C? What does this domain imply in terms of the number of anytime minutes?

(e) Describe the shape of the graph.

If the domain of fis all real numbers in the interval [0,7]and the domain of g is all real numbers in the interval [-2,5], the domain of f+gis all real numbers in the interval _________.
See all solutions

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