Question

a chart from dick’s sporting goods gives the recommended bat length b in inches for a man weighing between 165 and 170 pounds as a function of his height h in inches. the table is partially reproduced below:

h (height)	b (bat length)
49–52	31
53–56	33
57–60	32
61–64	33
65–68	33
69–72	33
73+	33

(a) explain in practical terms the meaning of ( f(63) ).

• ( f(63) ) is the weight of a man if his recommended bat length is 33 and his height is 63 inches.
• ( f(63) ) is the recommended bat length for a man weighing between 165 and 170 pounds if his height is 58 inches.
• ( f(63) ) is the height of a man weighing between 165 and 170 pounds if his recommended bat length is 63 inches.
• ( f(63) ) is the recommended bat length for a man weighing between 165 and 170 pounds if his height is 63 inches.
• ( f(63) ) is the height of a man weighing 63 pounds if his recommended bat length is between 165 and 170 inches.

(b) give the value of ( f(58) ).
(\boxed{quad}) in
(c) use functional notation to express the recommended bat length for a man weighing between 165 and 170 pounds if his height is 58 inches.
( fleft( \boxed{quad}
ight) )

Explanation:

Part (a) - Interpreting \( B(63) \)

The function \( B(h) \) gives the recommended bat length \( B \) (in inches) for a man (weighing 165 - 170 lbs) as a function of his height \( h \) (in inches). So \( B(63) \) means we substitute \( h = 63 \) into the function \( B \), which represents the recommended bat length for a man (in the weight range) with height 63 inches. Looking at the options, the correct interpretation is: \( B(63) \) is the recommended bat length for a man weighing between 165 and 170 pounds if his height is 63 inches.

Part (b) - Finding \( B(58) \)

Step 1: Identify the height range for \( h = 58 \)

From the table, the height range \( 57 - 60 \) includes \( h = 58 \).

Step 2: Find the corresponding bat length

In the table, for the height range \( 57 - 60 \), the bat length \( B \) is 32 inches. So \( B(58) = 32 \) (since 58 is in the 57 - 60 height range, we use the associated bat length).

Part (c) - Functional Notation

We need to express the recommended bat length for a man (165 - 170 lbs) with height 58 inches using functional notation. The function is \( B(h) \), where \( h \) is the height. So we substitute \( h = 58 \) into \( B \), giving \( B(58) \).

Answer:

s:
(a) \( B(63) \) is the recommended bat length for a man weighing between 165 and 170 pounds if his height is 63 inches.
(b) \( \boldsymbol{32} \)
(c) \( B\boldsymbol{(58)} \)