Question

What is the domain and range of the problem? How many beats will she have in half an hour? Is the graph discrete or continuous? What label goes on the side of the graph and which goes on the bottom?

Answer 1

From the statement, we know that Miss Butterkey's heart rate is 80 beats per minute.

So the ratio of beats per minute is:

`r=80\cdot\frac{\text{beats}}{\min }\text{.}`

The number of beats as a function of time is given by the product:

`b(M)=r\cdot M\min =80\cdot(beats)/(\min)\cdot M\cdot\min =80M\cdot\text{beats.}`

Where t is the time in minutes.

(0) If we define:

• M = # of minutes,

,

• b = # of beats after M minutes.

Using the equation of b(t), we have:

`b=80M\text{ beats }\Rightarrow M(b)=(b)/(80)\text{.}`

(1) Domain and range

If we consider the independent variable as the number of minutes M, the domain is:

`\text{Domain = 0, 1, 2, 3, }\ldots\text{.}`

If we consider the dependent variable as the number of beats b, the range is:

`\text{Range = }0,80,160,240,\ldots\text{.}`

(2) # of beats after half an hour

After half an hour the time is t = 30 min. Replacing this value in the equation of b(t), we get:

`b(30\min )=80\cdot(beats)/(\min)\cdot30\cdot\min =2400\text{ beats.}`

(3) The graph of heartbeats as a function of the minutes is discrete. That's because we can only have an integer number of beats.

(4) Labels of the graph

• horizontal label: number of minutes M,

,

• vertical label: number of beats b.

(5) Graph

Answers

• (0), M(b) = b/80

,

• (1) ,Domain = 0, 1, 2, 3, ... , Range = 0, 80, 160, 240, ...

,

• (2), b(30 min) = 2400 beats

,

• (3), The graph is discrete.

,

• (4) ,Horizontal label: # of minutes M, Vertical label: # of beats

,

• (5), Graph